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Find the linear function with f(1) = 4 and slope 6.

Select one:

- f(x) = 4x + 6
- f(x) = 6x – 2
- f(x) = 6x + 4
- f(x) = 6x + 4x
- f(x) = 6x
^{2}– 2

The correct answer is: f(x) = 6x – 2

Question **2**

If f (t)=t^{2} + t, Between t = 10 and t = 12, what is the increase in f divided by the increase in t?

Select one:

- 2
- 46
- 23
- 1/23
- 25

The correct answer is: 23

Question **3**

If f (t)=t^{2} + t, find [ f(t + h) -f (t)]/h.

Select one:

- 2t + h + 1
- 2t + 1
- 2t
- 1
- Undefined

The correct answer is: 2t + h + 1

Question **4**

On a circle of radius R find the x and y coordinates at time t (and angle t).

Select one:

- (cos t, sin t)
- (t cos 3, t sin 3)
- (sin t, cos t)
- (Rcos t, Rsin t)
- (t cos R, t sin R)

The correct answer is: (Rcos t, Rsin t)

Question **5**

From the formula for sin (2t + t) find sin 3t in terms of sin t.

Select one:

- 3sin(t)cos(t)
- 2sin(t) + sin
^{2}(t) - sin
^{2}(t) + 3sin (t) - 6sin (t) cos (t)
- -4 sin
^{3}(t) + 3sin (t)

The correct answer is: -4 sin^{3} (t) + 3sin (t)

Which function has the same slope as g(x)= x^{2}?

Select one:

- f(x) = (1/2)x
^{2} - f(x) = 4x
^{2} - f(x) = x
^{2}+ 3 - f(x) = 2x
- f(x) = 2

The correct answer is: f(x) = x^{2}+ 3

Question **2**

What is the tangent line to f(x) = x^{2} + 3 at (4,19)?

Select one:

- y = 8x - 13
- y = -2x+ 5
- y = 4x + 19
- y = 19x + 4
- y = 2

The correct answer is: y = 8x - 13

Question **3**

What is the derivative of f(x) = (x^{2} + 1)^{2} at (3, 100)?

Select one:

- 2x
^{2}+ 2 - 120
- 100
- 2
- 3

Question **4**

The tangent line to y = x^{3} + 6x at the origin is?

Select one:

- y = 3x + 6
- y = 3
- y= 6
- y = 6x + 3
- y = 6x

The correct answer is: y = 6x

Question **5**

What is Lim (t^{2} - 4) / (t – 2)

t→2

Select one:

- 0
- 2
- 4
- 6
- Undefined

The correct answer is: 4

What is the derivative of f(x) times g(x), if f(x) = 2x + 1 and g(x) = x^{2}?

Select one:

- (1/2)x
^{2} - 6x
^{2}+ 2x - 8x
- 8
- 0

Question **2**

What is the derivative of f(x) divided by g(x), if f(x) = 2x + 1 and g(x) = x^{2}?

Select one:

- -2/x
^{2}- 2/x^{3} - 6x
^{2}+ 2x - 2x
^{2}+ 3 - 0
- Impossible

Question **3**

What is the derivative of f(x) = -cos x?

Select one:

- -cos x
- cos x
- sin x
- -sin x
- 0

Question **4**

The tangent line to y = 3 sin x + 2 at (pi, 2) is:

Select one:

- y = 3x + 6
- y = -3x +5
- y= -3
- y = -3x -6
- y = -3x + 3pi +2

Question **5**

Why is f(x) = { 5 for x >0

3 for x = 0

5 for x < 0

not continuous at x = 0?

Select one:

- Because f(x) is not defined at x = 0
- Because f(x) is not differentiable at x = 0
- Because the left hand limit does not equal the right hand limit as x goes to 0
- Because f(0) does not equal both (or either) the left hand limit and/or the right hand limit
- It is continuous at x = 0

What is the derivative of f(x) = 5xe^{3x} at the point (0, 0)?

Select one:

- 0
- 5
- 10
- 15
- 3

Question **2**

What is the tangent line to f(x) = (e^{z} +3)^{2} at (0, 16)?

Select one:

- y = -6x + 16
- y = 6x + 16
- y = 16
- y = 6x + 9
- y = 2

Question **3**

What is the derivative of f(x) = ln (3x +1)?

Select one:

- f’(x) = 3 / (3x + 1)
- f’(x) = 1/(3x + 1)
- f’(x) = 3/ (ln (3x + 1))
- f’(x) = 1/ (ln (3x+ 1))
- Impossible

Question **4**

How long will it take $10,000 to compound continuously to $30,000 at 7% interest? Choose the closest answer.

Select one:

- About 5 years
- About 10 years
- About 15 years
- About 20 years
- Never

Question **5**

The half life of Carbon-14 is 5,730 years (i.e., it decays so that only have remains after 5,730 years). How long until 16 grams of Carbon-14 decays into 4 grams?

Select one:

- 1,000 years
- 5,730 years
- 11,460 years
- A million years
- Undefined

What is the linear approximation to f(x) = sin x, , near x = pi/2?

Select one:

- y =cos x
- y = 0
- y = 1
- y = pi/2
- y = pi/2 + 1

The correct answer is: y = 1

Question **2**

The local maximum of f(x)=x^{3} - 9x occurs at what value of x?

Select one:

- 0
- 3
- -3
- the square root of 3
- –(the square root of 3)

The correct answer is: –(the square root of 3)

Question **3**

Where is f(x) = x^{3} - 6x^{2} concave down?

Select one:

- (-infinity, 2)
- (2, infinity)
- (-infinity, infinity)
- (-2, 2)
- (-infinity, -2)

The correct answer is: (-infinity, 2)

Question **4**

Find all points 0 <c <2 where f (2) -f (0) =f '(c)(2 -0), for f(x)= 1 +x+x^{2}.

Select one:

- c =3
- c =2
- c = 1
- c =0
- There are no such points

The correct answer is: c = 1

Question **5**

What is Lim (x – pi) / (sin x)?

t→pi

Select one:

- 1
- 0
- -1
- Infinity
- Undefined

The correct answer is: -1

What is the derivative of f(x) = (x + sin x)^{3}?

Select one:

- f’(x) = 3(1 + cos x)
^{2} - f’(x) = 3(1 + sin x)
^{2} - f’(x) = 1 + cos x
- f(x) = 3(1+ cos x)(x + sin x)
^{2} - Impossible

The correct answer is: f(x) = 3(1+ cos x)(x + sin x)^{2}

Question **2**

What is the tangent line to f(x) = (x^{3} + 3x – 5)^{4} at (1,1)?

Select one:

- y = -24x + 25
- y = 25x -24
- y = 1x + 1
- y = 1
- Impossible

The correct answer is: y = -24x + 25

Question **3**

What is the derivative of f(x) = (x^{2} + 1)^{2} at (3, 100)?

Select one:

- 2x
^{2}+ 2 - 120
- 100
- 2
- 3

Question **4**

If x^{2} y + xy^{2} = 1, what is y’?

Select one:

- y’ = 0
- y’ = -1/2x
- y’ = (-2xy – x
^{2}) / (y^{2}+ 2xy) - y’ = (y
^{2}+ 2xy) / (-2xy – x^{2}) - y’ is undefined

The correct answer is: y’ = (y^{2} + 2xy) / (-2xy – x^{2})

Question **5**

Consider the circle x^{2} + y^{2} = 9. What is the tangent line to this circle at (3, 0)?

Select one:

- y =0
- x = 3
- y = x
^{2}- 9 - x = 0
- Undefined

The correct answer is: x = 3

MATH 1211: CALCULUS

Which is the general ant derivative of f(x) = 4x + sin x?

Select one:

a. 2x2 + cos x + C

b. 2x2 - cos x + C

c. 2x2 + sin x + C

d. 2x2 – sin x + C

e. None of these

The correct answer is: 2x2 - cos x + C

Question 2

Question text

Why does Newton’s Method not work to find the solutions of f(x) = x2 + 1?

Select one:

a. Because f(x) is not a function

b. Because there are no solutions

c. Because the solutions are negative

d. Because the solutions are imaginary

e. Because f(x) has no derivative

The correct answer is: Because the solutions are imaginary

Question 3

Question text

What is the antiderivative of f(x) = 5x4– 4x3 + 2 where f(0) = 5?

Select one:

a. x5– x4 + 2x + 5

b. 5x4– 3x3 + 7

c. 5x5– 3x4 + 2

d. 2x5– (3/2)x4 + C

e. x5– x4 + C

The correct answer is: x5– x4 + 2x + 5

Question 4

Question text

If fn = n2, what is the sum of the first four values of n, n = 1, 2, 3, and 4?

Select one:

a. 10

b. 20

c. 30

d. 40

e. None of these

The correct answer is: 30

Question 5

Question text

What is the area under the graph of f(x) = 2x, between x = 3 and x = 4? You might want to draw a picture.

Select one:

a. 0

b. 1

c. 3

d. 5

e. 7

The correct answer is: 7

If x2y + xy2 = 1, what is y’?

Select one:

a. y’ = 0

b. y’ = -1/2x

c. y’ = (-2xy – x2) / (y2 + 2xy)

d. y’ = (y2 + 2xy) / (-2xy – x2)

e. y’ is undefined

The correct answer is: y’ = (y2 + 2xy) / (-2xy – x2)

Question 2

Question text

The local minimum of f(x)=x3 - 9x occurs at what value of x?

Select one:

a. 0

b. 3

c. -3

d. the square root of 3

e. –(the square root of 3)

The correct answer is: the square root of 3

Question 3

Question text

What is the derivative of f(x) = ex sin x?

Select one:

a. f’(x) = ex cos x

b. f’(x) = cos x

c. f’(x) =ex sin x + ex cos x

d. f’(x) = ex sin x – ex cos x

e. Impossible

The correct answer is: f’(x) =ex sin x + ex cos x

Question 4

Question text

What is the derivative of f(x) = ex ln x?

Select one:

a. f’(x) = ex ln x

b. f’(x) = ex/x

c. f’(x) =ex lnx + ex/x

d. f’(x) = ex lnx – ex/x

e. Impossible

The correct answer is: f’(x) =ex lnx + ex/x

Question 5

Question text

Where is f(x) = 2x3 + 12x2 + 3x + 7 concave down?

Select one:

a. (-∞, -6)

b. (-6, ∞)

c. (-∞, ∞)

d. (-6, 6)

e. Never

The correct answer is: (-∞, -6)

Question 6

Question text

What is the derivative of f(x) = (x2 -2 + ex)2 at (0, 1)?

Select one:

a. -2

b. -1

c. 0

d. 1

e. 2

The correct answer is: -2

Question 7

Question text

The local maximum of f(x)=x3 - 9x occurs at what value of x?

Select one:

a. 0

b. 3

c. -3

d. the square root of 3

e. –(the square root of 3)

The correct answer is: –(the square root of 3)

Question 8

Question text

What is the linear approximation to f(x) = 5 ln (1 + x)2 at (0, 0)?

Select one:

a. y = 10x

b. y = x

c. y = -x

d. y = -10x

e. Undefined

The correct answer is: y = 10x

Question 9

Question text

How long will it take $5,000 to compound continuously to $30,000 at 8% interest? Choose the closest answer.

Select one:

a. About 8 years

b. About 15 years

c. About 22 years

d. About 30 years

e. Never

The correct answer is: About 22 years

Question 10

Question text

What is the linear approximation to f(x) = 2cos x, near x = pi/2?

Select one:

a. y =1

b. y =1x

c. y =-2

d. y =-2x

e. y = -2x + pi

The correct answer is: y = -2x + pi

What is the derivative of f(x) = 5xe3x at the point (0, 0)?

Select one:

a. 0

b. 5

c. 10

d. 15

e. 3

The correct answer is: 5

Question 2

Question text

What is the tangent line to f(x) = (ez +3)2 at (0, 16)?

Select one:

a. y = -6x + 16

b. y = 6x + 16

c. y = 16

d. y = 6x + 9

e. y = 2

The correct answer is: y = 6x + 16

Question 3

Question text

What is the derivative of f(x) = ln (3x +1)?

Select one:

a. f’(x) = 3 / (3x + 1)

b. f’(x) = 1/(3x + 1)

c. f’(x) = 3/ (ln (3x + 1))

d. f’(x) = 1/ (ln (3x+ 1))

e. Impossible

The correct answer is: f’(x) = 3 / (3x + 1)

Question 4

Question text

How long will it take $10,000 to compound continuously to $30,000 at 7% interest? Choose the closest answer.

Select one:

a. About 5 years

b. About 10 years

c. About 15 years

d. About 20 years

e. Never

The correct answer is: About 15 years

Question 5

Question text

The half life of Carbon-14 is 5,730 years (i.e., it decays so that only have remains after 5,730 years). How long until 16 grams of Carbon-14 decays into 4 grams?

Select one:

a. 1,000 years

b. 5,730 years

c. 11,460 years

d. A million years

e. Undefined

The correct answer is: 11,460 years

What is the derivative of f(x) = (x + sin x)3?

Select one:

a. f’(x) = 3(1 + cos x)2

b. f’(x) = 3(1 + sin x)2

c. f’(x) = 1 + cos x

d. f(x) = 3(1+ cos x)(x + sin x)2

e. Impossible

The correct answer is: f(x) = 3(1+ cos x)(x + sin x)2

Question 2

Question text

What is the tangent line to f(x) = (x3 + 3x – 5)4 at (1,1)?

Select one:

a. y = -24x + 25

b. y = 25x -24

c. y = 1x + 1

d. y = 1

e. Impossible

The correct answer is: y = -24x + 25

Question 3

Question text

What is the derivative of f(x) = (x2 + 1)2 at (3, 100)?

Select one:

a. 2x2 + 2

b. 120

c. 100

d. 2

e. 3

The correct answer is: 120

Question 4

Question text

If x2 y + xy2 = 1, what is y’?

Select one:

a. y’ = 0

b. y’ = -1/2x

c. y’ = (-2xy – x2) / (y2 + 2xy)

d. y’ = (y2 + 2xy) / (-2xy – x2)

e. y’ is undefined

The correct answer is: y’ = (y2 + 2xy) / (-2xy – x2)

Question 5

Question text

Consider the circle x2 + y2 = 9. What is the tangent line to this circle at (3, 0)?

Select one:

a. y =0

b. x = 3

c. y = x2 - 9

d. x = 0

e. Undefined

The correct answer is: x = 3

What is the linear approximation to f(x) = sin x, , near x = pi/2?

Select one:

a. y =cos x

b. y = 0

c. y = 1

d. y = pi/2

e. y = pi/2 + 1

The correct answer is: y = 1

Question 2

Question text

The local maximum of f(x)=x3 - 9x occurs at what value of x?

Select one:

a. 0

b. 3

c. -3

d. the square root of 3

e. –(the square root of 3)

The correct answer is: –(the square root of 3)

Question 3

Question text

Where is f(x) = x3 - 6x2 concave down?

Select one:

a. (-infinity, 2)

b. (2, infinity)

c. (-infinity, infinity)

d. (-2, 2)

e. (-infinity, -2)

The correct answer is: (-infinity, 2)

Question 4

Question text

Find all points 0 <c <2 where f (2) -f (0) =f '(c)(2 -0), for f(x)= 1 +x+x2.

Select one:

a. c =3

b. c =2

c. c = 1

d. c =0

e. There are no such points

The correct answer is: c = 1

Question 5

Question text

What is Lim (x – pi) / (sin x)?

t→pi

Select one:

a. 1

b. 0

c. -1

d. Infinity

e. Undefined

The correct answer is: -1

The tangent line to y = x + sin x at the origin is:

Select one:

a. y = 2x

b. y = 3x - 3

c. y= -2x

d. y = x + pi

e. y = 6x

The correct answer is: y = 2x

Question 2

Question text

Which function has the same slope as g(x)= x3 + 2?

Select one:

a. f(x) = (1/2)x3

b. f(x) = x3 -5

c. f(x) = x2+ 3

d. f(x) = 3x

e. f(x) = 2

The correct answer is: f(x) = x3 -5

Question 3

Question text

What is Lim (t2 - 16) / (t + 4) as t goes to -4?

Select one:

a. 0

b. -4

c. 4

d. -8

e. Undefined

The correct answer is: -8

Question 4

Question text

What is Lim (t2 + 9) / (t – 3)?

t→3

Select one:

a. 3

b. -3

c. 6

d. -6

e. Undefined

The correct answer is: Undefined

Question 5

Question text

Which function has the same slope as g(x)= 5x4 + 2?

Select one:

a. f(x) = (1/2)x3

b. f(x) = 5x4 -9

c. f(x) = x2+ 3

d. f(x) = 0

e. f(x) = 20

The correct answer is: f(x) = 5x4 -9

Question 6

Question text

What is the derivative of f(x) times g(x), if f(x) = sin (x) and g(x) = x2?

Select one:

a. 0

b. x2 (sin x ) - x cos x

c. 2x (sin x) + x2 (cos x)

d. 2x (sin x) - x2 (cos x)

e. sin x + cos x

The correct answer is: 2x (sin x) + x2 (cos x)

Question 7

Question text

What is the derivative of f(x) = (5x + 1)2 at (2, 121)?

Select one:

a. 0

b. 22

c. 100

d. 110

e. 220

The correct answer is: 110

Question 8

Question text

If f (t)=t2 + 4t + 3, find [ f(t + h) -f (t)]/h.

Select one:

a. 2h +2t + 2

b. 2t

c. 2t + h + 4

d. 2t + 4

e. Undefined

The correct answer is: 2t + h + 4

Question 9

Question text

The tangent line to y = 3x - cos x at the (0, -1) is?

Select one:

a. y = -1

b. y = 3x – 3

c. y= 3x -1

d. y = x + pi

e. y = 6x

The correct answer is: y= 3x -1

Question 10

Question text

What is the derivative of f(x) = (x2 + 1)2 at (2, 25)?

Select one:

a. 0

b. 2

c. 40

d. -6

e. 30

The correct answer is: 40

What is the derivative of f(x) times g(x), if f(x) = 2x + 1 and g(x) = x2?

Select one:

a. (1/2)x2

b. 6x2 + 2x

c. 8x

d. 8

e. 0

The correct answer is: 6x2 + 2x

Question 2

Question text

What is the derivative of f(x) divided by g(x), if f(x) = 2x + 1 and g(x) = x2?

Select one:

a. -2/x2 - 2/x3

b. 6x2 + 2x

c. 2x2 + 3

d. 0

e. Impossible

The correct answer is: -2/x2 - 2/x3

Question 3

Question text

What is the derivative of f(x) = -cos x?

Select one:

a. -cos x

b. cos x

c. sin x

d. -sin x

e. 0

The correct answer is: sin x

Question 4

Question text

The tangent line to y = 3 sin x + 2 at (pi, 2) is:

Select one:

a. y = 3x + 6

b. y = -3x +5

c. y= -3

d. y = -3x -6

e. y = -3x + 3pi +2

The correct answer is: y = -3x + 3pi +2

Question 5

Question text

Why is f(x) = { 5 for x >0

3 for x = 0

5 for x < 0

not continuous at x = 0?

Select one:

a. Because f(x) is not defined at x = 0

b. Because f(x) is not differentiable at x = 0

c. Because the left hand limit does not equal the right hand limit as x goes to 0

d. Because f(0) does not equal both (or either) the left hand limit and/or the right hand limit

e. It is continuous at x = 0

The correct answer is: Because f(0) does not equal both (or either) the left hand limit and/or the right hand limit

Find the linear function with f(1) = 4 and slope 6.

Select one:

a. f(x) = 4x + 6

b. f(x) = 6x – 2

c. f(x) = 6x + 4

d. f(x) = 6x + 4x

e. f(x) = 6x2 – 2

The correct answer is: f(x) = 6x – 2

Question 2

Question text

If f (t)=t2 + t, Between t = 10 and t = 12, what is the increase in f divided by the increase in t?

Select one:

a. 2

b. 46

c. 23

d. 1/23

e. 25

The correct answer is: 23

Question 3

Question text

If f (t)=t2 + t, find [ f(t + h) -f (t)]/h.

Select one:

a. 2t + h + 1

b. 2t + 1

c. 2t

d. 1

e. Undefined

The correct answer is: 2t + h + 1

Question 4

Question text

On a circle of radius R find the x and y coordinates at time t (and angle t).

Select one:

a. (cos t, sin t)

b. (t cos 3, t sin 3)

c. (sin t, cos t)

d. (Rcos t, Rsin t)

e. (t cos R, t sin R)

The correct answer is: (Rcos t, Rsin t)

Question 5

Question text

From the formula for sin (2t + t) find sin 3t in terms of sin t.

Select one:

a. 3sin(t)cos(t)

b. 2sin(t) + sin2 (t)

c. sin2 (t) + 3sin (t)

d. 6sin (t) cos (t)

e. -4 sin3 (t) + 3sin (t)

The correct answer is: -4 sin3 (t) + 3sin (t)

Which function has the same slope as g(x)= x2?

Select one:

a. f(x) = (1/2)x2

b. f(x) = 4x2

c. f(x) = x2+ 3

d. f(x) = 2x

e. f(x) = 2

The correct answer is: f(x) = x2+ 3

Question 2

Question text

What is the tangent line to f(x) = x2 + 3 at (4,19)?

Select one:

a. y = 8x - 13

b. y = -2x+ 5

c. y = 4x + 19

d. y = 19x + 4

e. y = 2

The correct answer is: y = 8x - 13

Question 3

Question text

What is the derivative of f(x) = (x2 + 1)2 at (3, 100)?

Select one:

a. 2x2 + 2

b. 120

c. 100

d. 2

e. 3

The correct answer is: 120

Question 4

Question text

The tangent line to y = x3 + 6x at the origin is?

Select one:

a. y = 3x + 6

b. y = 3

c. y= 6

d. y = 6x + 3

e. y = 6x

The correct answer is: y = 6x

Question 5

Question text

What is Lim (t2 - 4) / (t – 2)

t→2

Select one:

a. 0

b. 2

c. 4

d. 6

e. Undefined

The correct answer is: 4

What is the antiderivative of f(x) = 5x4– 4x3 + 2 where f(1) = 6?

Select one:

a. x5– x4 + 2x + 4

b. 5x4– 3x3 + 7

c. 5x5– 3x4 + 3

d. x5– x4 + 6

The correct answer is: x5– x4 + 2x + 4

Question 2

Question text

What is the tangent line to f(x) = (x2 + x – 3)4 at (1,1)?

Select one:

a. y = -12x + 13

b. y = 12x -24

c. y = 1x + 1

d. y = 1

e. Impossible

The correct answer is: y = -12x + 13

Question 3

Question text

Which is the general antiderivative of f(x) = 4x3 + sin 2x?

Select one:

a. 3x2 + cos 2x + C

b. x4 – (1/2)cos 2x + C

c. 2x2 + sin x + C

d. 2x2 – sin x + C

The correct answer is: x4 – (1/2)cos 2x + C

Question 4

Question text

What is Lim (x ) / (cos x)?

t→0

Select one:

a. 1

b. 0

c. -1

d. Infinity

e. Undefined

The correct answer is: 0

Question 5

Question text

What is ʃ e(1/2)x dx?

Select one:

a. e(1/2)x + C

b. 3 e(1/2)x + C

c. (1/2) e(1/2)x + C

d. 2 e(1/2)x + C

e. -2 e(1/2)x + C

The correct answer is: 2 e(1/2)x + C

Question 6

Question text

If f (t)=t2 + 3, find [ f(t + h) -f (t)]/h.

Select one:

a. 2t + h

b. 2t + 1

c. 2t

d. 1

e. Undefined

The correct answer is: 2t + h

Question 7

Question text

What is the derivative of f(x) = (x2 + 1)2 at (1, 4)?

Select one:

a. 2x2 + 2

b. 8

c. 4

d. 6

e. 0

The correct answer is: 8

Question 8

Question text

What is the derivative of f(x) = - cos 2x?

Select one:

a. – 2cos x

b. 2cos 2x

c. 2sin 2x

d. –2sin 2x

e. 0

The correct answer is: 2sin 2x

Question 9

Question text

If fn = (n+ 1)2, what is the sum of the first four values of n, n = 1, 2, 3, and 4?

Select one:

a. 10

b. 24

c. 34

d. 44

e. 54

The correct answer is: 54

Question 10

Question text

If F(x) satisfies F ’ (x) = f(x), and F(A) = 10, F(B) = 15, what is ʃ f(x)dx, if the limits of the integral are B (upper) and A (lower)?

Select one:

a. 0

b. 15

c. -5

d. 5

e. Impossible

The correct answer is: 5

What is the derivative of f(x) = (x2 + 1)2 at (1, 4)?

Select one:

a. 2x2 + 2

b. 8

c. 4

d. 6

e. 0

The correct answer is: 8

Question 2

Question text

What is the derivative of f(x) = - cos 2x?

Select one:

a. – 2cos x

b. 2cos 2x

c. 2sin 2x

d. –2sin 2x

e. 0

The correct answer is: 2sin 2x

Question 3

Question text

If fn = (n+ 1)2, what is the sum of the first four values of n, n = 1, 2, 3, and 4?

Select one:

a. 10

b. 24

c. 34

d. 44

e. 54

The correct answer is: 54

Question 4

Question text

What is the antiderivative of f(x) = 5x4– 4x3 + 2 where f(1) = 6?

Select one:

a. x5– x4 + 2x + 4

b. 5x4– 3x3 + 7

c. 5x5– 3x4 + 3

d. x5– x4 + 6

The correct answer is: x5– x4 + 2x + 4

Question 5

Question text

If f (t)=t2 + 3, find [ f(t + h) -f (t)]/h.

Select one:

a. 2t + h

b. 2t + 1

c. 2t

d. 1

e. Undefined

The correct answer is: 2t + h

Question 6

Question text

If F(x) satisfies F ’ (x) = f(x), and F(A) = 10, F(B) = 15, what is ʃ f(x)dx, if the limits of the integral are B (upper) and A (lower)?

Select one:

a. 0

b. 15

c. -5

d. 5

e. Impossible

The correct answer is: 5

Question 7

Question text

What is ʃ e(1/2)x dx?

Select one:

a. e(1/2)x + C

b. 3 e(1/2)x + C

c. (1/2) e(1/2)x + C

d. 2 e(1/2)x + C

e. -2 e(1/2)x + C

The correct answer is: 2 e(1/2)x + C

Question 8

Question text

Which is the general antiderivative of f(x) = 4x3 + sin 2x?

Select one:

a. 3x2 + cos 2x + C

b. x4 – (1/2)cos 2x + C

c. 2x2 + sin x + C

d. 2x2 – sin x + C

The correct answer is: x4 – (1/2)cos 2x + C

Question 9

Question text

What is Lim (x ) / (cos x)?

t→0

Select one:

a. 1

b. 0

c. -1

d. Infinity

e. Undefined

The correct answer is: 0

Question 10

Question text

What is the tangent line to f(x) = (x2 + x – 3)4 at (1,1)?

Select one:

a. y = -12x + 13

b. y = 12x -24

c. y = 1x + 1

d. y = 1

e. Impossible

The correct answer is: y = -12x + 13

What is ʃ e(1/2)x dx?

Select one:

a. e(1/2)x + C

b. 3 e(1/2)x + C

c. (1/2) e(1/2)x + C

d. 2 e(1/2)x + C

e. -2 e(1/2)x + C

The correct answer is: 2 e(1/2)x + C

Question 2

Question text

What is the antiderivative of f(x) = 5x4– 4x3 + 2 where f(1) = 6?

Select one:

a. x5– x4 + 2x + 4

b. 5x4– 3x3 + 7

c. 5x5– 3x4 + 3

d. x5– x4 + 6

The correct answer is: x5– x4 + 2x + 4

Question 3

Question text

What is the derivative of f(x) = (x2 + 1)2 at (1, 4)?

Select one:

a. 2x2 + 2

b. 8

c. 4

d. 6

e. 0

The correct answer is: 8

Question 4

Question text

If fn = (n+ 1)2, what is the sum of the first four values of n, n = 1, 2, 3, and 4?

Select one:

a. 10

b. 24

c. 34

d. 44

e. 54

The correct answer is: 54

Question 5

Question text

What is the derivative of f(x) = - cos 2x?

Select one:

a. – 2cos x

b. 2cos 2x

c. 2sin 2x

d. –2sin 2x

e. 0

The correct answer is: 2sin 2x

Question 6

Question text

Which is the general antiderivative of f(x) = 4x3 + sin 2x?

Select one:

a. 3x2 + cos 2x + C

b. x4 – (1/2)cos 2x + C

c. 2x2 + sin x + C

d. 2x2 – sin x + C

The correct answer is: x4 – (1/2)cos 2x + C

Question 7

Question text

What is Lim (x ) / (cos x)?

t→0

Select one:

a. 1

b. 0

c. -1

d. Infinity

e. Undefined

The correct answer is: 0

Question 8

Question text

If F(x) satisfies F ’ (x) = f(x), and F(A) = 10, F(B) = 15, what is ʃ f(x)dx, if the limits of the integral are B (upper) and A (lower)?

Select one:

a. 0

b. 15

c. -5

d. 5

e. Impossible

The correct answer is: 5

Question 9

Question text

If f (t)=t2 + 3, find [ f(t + h) -f (t)]/h.

Select one:

a. 2t + h

b. 2t + 1

c. 2t

d. 1

e. Undefined

The correct answer is: 2t + h

Question 10

Question text

What is the tangent line to f(x) = (x2 + x – 3)4 at (1,1)?

Select one:

a. y = -12x + 13

b. y = 12x -24

c. y = 1x + 1

d. y = 1

e. Impossible

The correct answer is: y = -12x + 13

If fn = (n+ 1)2, what is the sum of the first four values of n, n = 1, 2, 3, and 4?

Select one:

a. 10

b. 24

c. 34

d. 44

e. 54

The correct answer is: 54

Question 2

Question text

Which is the general antiderivative of f(x) = 4x3 + sin 2x?

Select one:

a. 3x2 + cos 2x + C

b. x4 – (1/2)cos 2x + C

c. 2x2 + sin x + C

d. 2x2 – sin x + C

The correct answer is: x4 – (1/2)cos 2x + C

Question 3

Question text

If f (t)=t2 + 3, find [ f(t + h) -f (t)]/h.

Select one:

a. 2t + h

b. 2t + 1

c. 2t

d. 1

e. Undefined

The correct answer is: 2t + h

Question 4

Question text

What is the derivative of f(x) = - cos 2x?

Select one:

a. – 2cos x

b. 2cos 2x

c. 2sin 2x

d. –2sin 2x

e. 0

The correct answer is: 2sin 2x

Question 5

Question text

What is the derivative of f(x) = (x2 + 1)2 at (1, 4)?

Select one:

a. 2x2 + 2

b. 8

c. 4

d. 6

e. 0

The correct answer is: 8

Question 6

Question text

What is the tangent line to f(x) = (x2 + x – 3)4 at (1,1)?

Select one:

a. y = -12x + 13

b. y = 12x -24

c. y = 1x + 1

d. y = 1

e. Impossible

The correct answer is: y = -12x + 13

Question 7

Question text

What is the antiderivative of f(x) = 5x4– 4x3 + 2 where f(1) = 6?

Select one:

a. x5– x4 + 2x + 4

b. 5x4– 3x3 + 7

c. 5x5– 3x4 + 3

d. x5– x4 + 6

The correct answer is: x5– x4 + 2x + 4

Question 8

Question text

What is ʃ e(1/2)x dx?

Select one:

a. e(1/2)x + C

b. 3 e(1/2)x + C

c. (1/2) e(1/2)x + C

d. 2 e(1/2)x + C

e. -2 e(1/2)x + C

The correct answer is: 2 e(1/2)x + C

Question 9

Question text

What is Lim (x ) / (cos x)?

t→0

Select one:

a. 1

b. 0

c. -1

d. Infinity

e. Undefined

The correct answer is: 0

Question 10

Question text

If F(x) satisfies F ’ (x) = f(x), and F(A) = 10, F(B) = 15, what is ʃ f(x)dx, if the limits of the integral are B (upper) and A (lower)?

Select one:

a. 0

b. 15

c. -5

d. 5

e. Impossible

The correct answer is: 5

If f (t)=t2 + 3, find [ f(t + h) -f (t)]/h.

Select one:

a. 2t + h

b. 2t + 1

c. 2t

d. 1

e. Undefined

The correct answer is: 2t + h

Question 2

Question text

If fn = (n+ 1)2, what is the sum of the first four values of n, n = 1, 2, 3, and 4?

Select one:

a. 10

b. 24

c. 34

d. 44

e. 54

The correct answer is: 54

Question 3

Question text

What is the antiderivative of f(x) = 5x4– 4x3 + 2 where f(1) = 6?

Select one:

a. x5– x4 + 2x + 4

b. 5x4– 3x3 + 7

c. 5x5– 3x4 + 3

d. x5– x4 + 6

The correct answer is: x5– x4 + 2x + 4

Question 4

Question text

What is ʃ e(1/2)x dx?

Select one:

a. e(1/2)x + C

b. 3 e(1/2)x + C

c. (1/2) e(1/2)x + C

d. 2 e(1/2)x + C

e. -2 e(1/2)x + C

The correct answer is: 2 e(1/2)x + C

Question 5

Question text

What is the tangent line to f(x) = (x2 + x – 3)4 at (1,1)?

Select one:

a. y = -12x + 13

b. y = 12x -24

c. y = 1x + 1

d. y = 1

e. Impossible

The correct answer is: y = -12x + 13

Question 6

Question text

What is the derivative of f(x) = (x2 + 1)2 at (1, 4)?

Select one:

a. 2x2 + 2

b. 8

c. 4

d. 6

e. 0

The correct answer is: 8

Question 7

Question text

What is Lim (x ) / (cos x)?

t→0

Select one:

a. 1

b. 0

c. -1

d. Infinity

e. Undefined

The correct answer is: 0

Question 8

Question text

Which is the general antiderivative of f(x) = 4x3 + sin 2x?

Select one:

a. 3x2 + cos 2x + C

b. x4 – (1/2)cos 2x + C

c. 2x2 + sin x + C

d. 2x2 – sin x + C

The correct answer is: x4 – (1/2)cos 2x + C

Question 9

Question text

What is the derivative of f(x) = - cos 2x?

Select one:

a. – 2cos x

b. 2cos 2x

c. 2sin 2x

d. –2sin 2x

e. 0

The correct answer is: 2sin 2x

Question 10

Question text

If F(x) satisfies F ’ (x) = f(x), and F(A) = 10, F(B) = 15, what is ʃ f(x)dx, if the limits of the integral are B (upper) and A (lower)?

Select one:

a. 0

b. 15

c. -5

d. 5

e. Impossible

The correct answer is: 5

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