Practice Problems for the Final Exam, Math 16a, Fall 2019

1. Find the x and y coordinates of the points on the curve

y 2+xy+x 2 = 4 where the curve has slope − 1 2 .

2. Use the definition of the derivate as a limit to evaluate the derivative of f(x) = 1/x2 .

3. For each of the following, find the limit value or determine that the limit does not exist.

(a) limx→3 x 3−x 2−6x x2−2x−3

(b) limx→∞ x 2−3x e x

4. Evaluate the first derivatives of the following functions.

(a) f(x) = ln(e √x) e ln(√x) (b) f(x) = x √ x

5. Use the derivative to approximate √
122. Hint: √
121 = 11.
6. Determine the following

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