Math 174 02,

the course of Dr. Mihailovs

Midterm 1

September 18, 1998

  1. Find $ f^{-1}$ for $ f(x)=3x+2$ .

  2. Prove that $ f(x)=x^7+x+1$ is one-to-one.

  3. Find $ g'(a)$ , where $ g$ is the inverse function of $ f(x)=x^7+x+1$ , $ a=3$.

  4. Find $ f'(x)$ for $ f(x)=e^{3x+2}$ .

  5. Evaluate $ \int e^{\cos x}\sin x\; dx$ .

  6. Find $ f'(x)$ for $ f(x)=\frac{e^{2x}\sqrt{3x+2}}{\sqrt[3]{x^2+2x+3}}$ .

  7. Evaluate $ \int_0^{\pi/2}\frac{\sin x}{1+\cos x}\; dx$ .

  8. Evaluate $ \int \frac{e^{2x}\: dx}{\sqrt{1-e^{4x}}}$ .

  9. Evaluate $ \int \frac{e^{2x}\: dx}{\sqrt{1+e^{4x}}}$ .

Copyright © 1998 Aleksandrs Mihailovs