Math 174 02,

the course of Dr. Mihailovs

Midterm 2

October 28, 1998

  1. Evaluate $ y'''-2y''-2y'-3y$ for $ y=e^{3x}$ .

  2. Find $ \underset{x\rightarrow 0}{\lim}\; \frac{\sin x-x}{x^3}$ .

  3. Evaluate $ \int \ln \left( x+\sqrt{x^2-1}\right) \; dx$ .

  4. Find $ \int \sin^6 x \cos^3 x \; dx$ .

  5. Find $ \int_0^3 \frac{x^3}{\sqrt{9-x^2}}\; dx$ .

  6. Find $ \int \frac{x^4+2x^3-8x+16}{x^3- 4x}\; dx$ .

  7. Evaluate $ \int \frac{dx}{1+\sqrt{3x-2}}$ .

  8. Solve the initial-value problem $ y'=\frac {y}{1+x^2}$ , $ y(0)=1$ .

  9. Use Simpson's Rule with $ n=4$ to estimate the length of the curve $ y=2\cos x$ , $ -\pi/3\leq x\leq \pi/3$ .

Copyright © 1998 Aleksandrs Mihailovs