Precalculus by Richard Wright

Are you not my student and
has this helped you?

This book is available

Therefore do not worry about tomorrow, for tomorrow will worry about itself. Each day has enough trouble of its own. Matthew‬ ‭6‬:‭34‬ ‭NIV‬‬‬‬

# 12-Review

Take this test as you would take a test in class. When you are finished, check your work against the answers. On this assignment round your answers to three decimal places unless otherwise directed.

Evaluate each limit.

1. $$\displaystyle \lim_{x \rightarrow 2} \frac{x-2}{x^2+3x-10}$$
2. $$\displaystyle \lim_{x \rightarrow 1} \frac{x^2+2}{x-4}$$
3. $$\displaystyle \lim_{x \rightarrow 4} \frac{\sqrt{x}-2}{x-4}$$
4. Use a table or graph to find the limit to 4 decimal places. Draw the table or graph.

5. $$\displaystyle \lim_{x \rightarrow π} \frac{3}{\sin x}$$
6. $$\displaystyle \lim_{x \rightarrow 2} \frac{x^3-8}{x-2}$$
7. Find the derivative.

8. f(x) = 4x + 3
9. f(x) = −3x2
10. $$f(x) = -\frac{2}{x^2}$$
11. Find the slope of $$f(x) = 2\sqrt{x}$$ at (9, 6).
12. Find the limit at infinity.

13. $$\displaystyle \lim_{x \rightarrow ∞} \frac{x(2x+3)}{5x^2-7x+1}$$
14. $$\displaystyle \lim_{x \rightarrow -∞} \frac{(2x+1)(3x-1)}{2x^3+5x-1}$$
15. $$\displaystyle \lim_{x \rightarrow ∞} \frac{(2x-3)(5x^2+1)}{(x+1)(x-3)}$$
16. Find the limit of the sequence.

17. $$a_n = \frac{7n^2-2n}{6n^2}$$
18. $$a_n = \frac{2n+1}{4n^2}$$
19. Find the area between the graph and the x-axis for the given interval of x.

20. f(x) = 5x2x     [1, 3]
21. f(x) = 2x     [−1, 3]
22. The equation v = −9.8t + 10 models the velocity of a ball thrown upwards at 10 m/s.

23. The derivative of velocity is the acceleration. Find the acceleration of the ball at t = 3 seconds.
24. Displacement is the integral of the velocity graph. Find the displacement of the ball between t = 0 and t = 3 seconds.

1. $$\frac{1}{7}$$
2. −1
3. $$\frac{1}{4}$$
4. Does not exist
5. 12
6. f –1(x) = 4
7. f –1(x) = –6x
8. $$f^{-1}(x) = \frac{4}{x^3}$$
9. $$\frac{1}{3}$$
10. $$\frac{2}{5}$$
11. 0
12. Does not exist
13. $$\frac{7}{6}$$
14. 0
15. $$\frac{118}{3}$$
16. 8
17. −9.8 m/s2
18. −14.1 m