MTH 1733 -- Honors Calculus 1 -- Fall 1997

Quiz 3

(6 points) For each of the following curves, determine the equations of the asymptotes, if any:
- $\displaystyle{y=\frac{2}{e^x-1}+3}$
- $\displaystyle{y=\ln (x^2 -4)}$
- $\displaystyle{y=e^{-\displaystyle{x^2}}}$
(6 points) Differentiate the following functions:
- $y=\displaystyle{x\sqrt{\ln x}}$
- $y=\displaystyle{e^{\displaystyle{e^{x^2}}}}$
- $y=\displaystyle{\frac{e^x+1}{x^e-1}}$
(8 points) Solve the following initial value problem:
$\begin{displaymath} y''-9y=0,\quad y(0)=8,\quad y'(0)=2.\end{displaymath}$
(10 points) For each of the following non-homogeneous differential equations with constant coefficients, write down the general form of the solution. You may leave the undetermined coefficients of the particular solution unevaluated, as in the following example.

y'+y=2x+3 Solution: y_h=C₁e^-x, y_p=Ax+B, y=y_h+y_p.
- y'-3y=4x³-5x²
- y'-3y=e^3x+x+3
- y'-3y=2e^-3x-3e^2x
- y''-y'=e^x
- y''-y'=1

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Created by Alexandru Suciu, Fri Nov 7, 1997

http://www.math.neu.edu/~suciu/mth1733/1733f97.q3/index.html