Math 173 02,

the course of Dr. Mihailovs

Midterm 1

February 19, 1999

  1. Find $ \underset{x\rightarrow 1}{\lim}\; \frac{x^2+2x-3}{x^2-1}$ .

  2. Find $ \underset{x\rightarrow 2}{\lim}\; \frac{\sqrt{2x}-\sqrt{x+2}}{\sqrt{3x-2}-\sqrt{x+2}}$ .

  3. Use the Squeeze Theorem to find $ \underset{x\rightarrow 0}{\lim}\; x^2 \sin\frac{\pi}{2x}$ .

  4. Find $ f'(x)$ for $ f(x)=\frac{2\sqrt{x}}{1+x}$ .

  5. Find $ f'(x)$ for $ f(x)=\cos (2x+3)$ .

  6. Find an equation of the tangent line to the curve $ y=x\tan 3x+\sin 2x$ at the point $ (0,0)$.

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

  8. Find the $ 100$th derivative of $ f(x)=x^{91}-2x^{19}+1$ .

  9. Find an approximate value for $ \sqrt{102}$ .

Copyright © 1998 Aleksandrs Mihailovs