Description

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