Mathematics Quiz

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

Select one:

  1. f(x) = 4x + 6
  2. f(x) = 6x – 2 
  3. f(x) = 6x + 4
  4. f(x) = 6x  + 4x
  5. f(x) = 6x2– 2

The correct answer is: f(x) = 6x – 2

Question 2

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:

  1. 2
  2. 46
  3. 23 
  4. 1/23
  5. 25

The correct answer is: 23

Question 3

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

Select one:

  1. 2t + h + 1 
  2. 2t + 1
  3. 2t
  4. 1
  5. 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:

  1. (cos t, sin t)
  2. (t cos 3, t sin 3)
  3. (sin t, cos t)
  4. (Rcos t, Rsin t) 
  5. (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:

  1. 3sin(t)cos(t)
  2. 2sin(t) + sin2(t)
  3. sin2(t) + 3sin (t)
  4. 6sin (t) cos (t)
  5. -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:

  1. f(x) = (1/2)x2
  2. f(x) = 4x2
  3. f(x) = x2+ 3 
  4. f(x) = 2x
  5. f(x) =  2

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

Question 2

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

Select one:

  1. y = 8x - 13 
  2. y = -2x+ 5
  3. y = 4x + 19
  4. y = 19x + 4
  5. y = 2

The correct answer is: y = 8x - 13

Question 3

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

Select one:

  1. 2x2+ 2
  2. 120 
  3. 100
  4. 2
  5. 3

Question 4

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

Select one:

  1. y = 3x + 6
  2. y = 3
  3. y= 6
  4. y = 6x + 3
  5. y = 6x 

The correct answer is: y = 6x

Question 5

What is Lim (t2 - 4) /  (t – 2)
              t→2

Select one:

  1. 0
  2. 2
  3. 6
  4. Undefined

The correct answer is: 4

Top of Form

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

Select one:

  1. (1/2)x2
  2. 6x2+ 2x 
  3. 8x
  4. 8
  5. 0

Question 2

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

Select one:

  1. -2/x2-  2/x3
  2. 6x2+ 2x
  3. 2x2+ 3
  4. 0
  5. Impossible

Question 3

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

Select one:

  1. -cos x
  2. cos x
  3. sin x 
  4. -sin x
  5. 0

Question 4

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

Select one:

  1. y = 3x + 6
  2. y = -3x +5
  3. y= -3
  4. y = -3x -6
  5. 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:

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

Bottom of Form

 

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

Select one:

  1. 0
  2. 10
  3. 15
  4. 3

Question 2

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

Select one:

  1. y = -6x + 16
  2. y = 6x + 16 
  3. y = 16
  4. y = 6x + 9
  5. y = 2

Question 3

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

Select one:

  1. f’(x) = 3 / (3x + 1) 
  2. f’(x) = 1/(3x + 1)
  3. f’(x) = 3/ (ln (3x + 1))
  4. f’(x) = 1/ (ln (3x+ 1))
  5. 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:

  1. About 5 years
  2. About 10 years
  3. About 15 years 
  4. About 20 years
  5. 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. 1,000 years
  2. 5,730 years
  3. 11,460 years 
  4. A million years
  5. Undefined

 

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

Select one:

  1. y =cos x
  2. y = 0
  3. y = 1 
  4. y = pi/2
  5. y = pi/2 + 1

The correct answer is: y = 1

Question 2

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

Select one:

  1. 0
  2. -3
  3. the square root of 3
  4. –(the square root of 3)

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

Question 3

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

Select one:

  1. (-infinity, 2)
  2. (2, infinity)
  3. (-infinity, infinity) 
  4. (-2, 2)
  5. (-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+x2.

Select one:

  1. c =3
  2. c =2
  3. c = 1 
  4. c =0
  5. 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. 1
  2. -1
  3. Infinity
  4. Undefined

The correct answer is: -1

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

Select one:

  1. f’(x) = 3(1 + cos x)2
  2. f’(x) = 3(1 + sin x)2
  3. f’(x) = 1 + cos x
  4. f(x) = 3(1+ cos x)(x + sin x)2
  5. 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) = (x3  + 3x – 5)4   at (1,1)?

Select one:

  1. y = -24x + 25
  2. y = 25x -24 
  3. y = 1x + 1
  4. y = 1
  5. Impossible

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

Question 3

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

Select one:

  1. 2x2+ 2
  2. 120 
  3. 100
  4. 2
  5. 3

Question 4

If  x2 y + xy2 = 1, what is y’?

Select one:

  1. y’ = 0
  2. y’ = -1/2x
  3. y’ = (-2xy – x2) / (y2+ 2xy)
  4. y’ = (y2+ 2xy) / (-2xy – x2
  5. y’ is undefined

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

Question 5

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

Select one:

  1. y =0
  2. x = 3
  3. y = x2- 9 
  4. x = 0
  5. 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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