Math 173 04,

the course of Dr. Mihailovs

Midterm 1

September 18, 1998

  1. Find $ \underset{x\rightarrow 1}{\lim}\; (3x+2)$ .

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

  3. Find $ \underset{x\rightarrow 4}{\lim}\; \frac{\sqrt{x}-2}{x-4}$ .

  4. Find $ \underset{x\rightarrow 1}{\lim}\; \frac{\sqrt{4x}-\sqrt{3x+1}}{\sqrt{2x+2}-\sqrt{x+3}}$ .

  5. Find vertical asymptotes for $ y=\frac{1}{x^2+x}$ .

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

  7. Find $ f'(x)$ for $ f(x)=x^7+x+1$ .

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

  9. Find an equation of the tangent line to the curve $ y=x^4+x$ at the point $ (0, 0)$ .

Copyright © 1998 Aleksandrs Mihailovs