Math 173 04,

the course of Dr. Mihailovs

Midterm 2

October 28, 1998

  1. Find $ f'(x)$ for $ f(x)=\sin (3x+2)$ .

  2. Find an equation of the tangent line to the curve $ y=x^4\tan 2x-x\cos 3x$ at the point $ (0,0)$.

  3. Find $ y'$ if $ x^2+y^4=3$.

  4. Find the $ 100$th derivative of $ f(x)=x^{73}-2x^{61}+137$ .

  5. Find an approximate value for $ \sqrt{25.1}$ .

  6. Find maximum and minimum values of $ f(x)=\frac{4x+3}{x^2+1}$ , $ -3\leq x\leq 1$ .

  7. Sketch the graph of $ y=\frac{x^3}{x^2-3}$ .

  8. Find $ f(x)$ if $ f'(x)=\sqrt[4]{x}+\cos 2x$ .

  9. Find $ f(x)$ if $ f'''(x)=12$ , $ f(0)=6$ , $ f'(0)=8$ , $ f''(0)=10$ .

Copyright © 1998 Aleksandrs Mihailovs