Gateway 3 Practice Test Fall Semester 1997-1998

NO CALCULATORS MAY BE USED ON THIS TEST. SHOW YOUR WORK. YOU DO NOT HAVE TO SIMPLIFY YOUR ANSWERS. EACH PROBLEM IS WORTH 10 POINTS.

IN 1 - 7, FIND THE DERIVATIVE.

1.

$${y = 6\ln(2x^2 + x)}$$

2.

$${s = 2e^{t^2-3t+1}}$$

3.

$${v = 2^{3u}}$$

4.

$${y = x^2(x-1)^{\sqrt{3}}}$$

5.

$${x^{(x^2)}}$$

6.

$${\theta = 3\sin^{-1}(\frac{t}{2})}$$

7.

$${z = 2\tan^{-1}(y^2)}$$

8.

Find the limit: $${\lim_{x\rightarrow 0}\frac{2\sin(x)}{3x}}$$

9.

Find the limit: $${\lim_{u\rightarrow\infty}\frac{3\ln(2u)+ 3u}{4u}}$$

10.

Find the limit: $${\lim_{t\rightarrow\infty}\frac{t^2+7t-1}{3e^t}}$$

NOTE: More space will be provided on the actual test.