Gateway 5 Practice Test Fall Semester 1997-1998

NO CALCULATORS MAY BE USED ON THIS TEST. SHOW YOUR WORK. (More space will be provided on the actual test.)

1.

(10 pts.) Find f(x). $${f'(x) = e^x-\sin(x), f(0)= 1}$$

2.

(20 pts.) Find s(t). $${s''(t) = -1, s'(0)= 3, s(0) = 7}$$

3.

(10 pts.) Evaluate $${\int_0^1 (x^2-2x+2)\; dx}$$

4.

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

5.

(10 pts.) Evaluate $${\int_1^e\left(\frac{3}{x}\right)\;dx}$$

6.

(10 pts.) Evaluate $${\int_0^{\pi/2}2\cos(\theta)\;d\theta}$$

7.

(10 pts.) Evaluate $${\int_0^{1/2}\frac{1}{2\sqrt{1-u^2}}\;du}$$

8.

(10 pts.) Evaluate $${\int3^x\;dx}$$

9.

(10 pts.) Find $${F^\prime}(x)$$. $${F(x) = \int_0^xe^{-t^2}\;dt}$$

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