Calculus I - Spring 2014

Midterm Exam II, April 21, 2014

1. If f(x) = x + cos x, then (f −1 ) ′ (1) is

2. Let f(x) = 1 − 2 3√x, then f −1 (x) is

3. Compute the linearization of f(x) = √xex−1 at a = 1.

4. If f(x) = (2 − x) x , then f ′ (x) is

5. Find the slope of the tangent line at the point (1, 1) on the graph of e x−y = 2x 2 − y2.

6. If f(x) = 21+arctan x , then f ′ (x) is

7. Find the differential of f(x) = √1 − 2x.

8. Let f(x) = arcsin x, then f −1 (x) is

9. Find lim x→ √ 3 + 5 1/(3−x 2).

10. Find lim x→ √ 3 + 5 1/(x 2−3).