Intro to Trig
Chapter 15
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TEST
Some Helpful Information
𝑥 3 + 𝑎3 = 𝑥 + 𝑎 𝑥 2 − 𝑎𝑥 + 𝑎2
𝑥 3 − 𝑎3 = 𝑥 − 𝑎 𝑥 2 + 𝑎𝑥 + 𝑎2
Evaluate each limit.
1. lim𝑥→2 −4𝑥 2 − 3𝑥 + 6
3. lim𝑥→5
5. lim𝑥→3
𝑥 2 −25
𝑥−5
2𝑥 2 −3𝑥
𝑥 3 −2𝑥 2 +𝑥+6
2. lim𝑥→𝜋
4. lim𝑥→3
6. lim𝑥→4
sin 𝑥
𝑥
𝑥 2 −3𝑥
𝑥 2 +2𝑥−15
2𝑥−8
𝑥 3 −64
Use a graphing calculator to find the value of each limit. Use radians
with trigonometric functions.
7. lim𝑥→0
𝑡𝑎𝑛 2𝑥
9. lim𝑥→1
1− 𝑥
8. lim𝑥→1
𝑥
ln 𝑥
ln 2𝑥−1
10. lim𝑥→0
𝑥−1
3𝑥−sin 3𝑥
𝑥 2 sin 𝑥
Use the derivative rules to find the derivative of each function.
11. 𝑓 𝑥 = 3𝑥 + 2
12. 𝑓 𝑥 = 𝑥 2 + 𝑥
14. 𝑓 𝑥 = −𝑥 3 − 2𝑥 2 + 3𝑥 + 6
13. 𝑓 𝑥 = 2𝑥 2 − 3𝑥 + 5
15. 𝑓 𝑥 = 3𝑥 4 + 2𝑥 3 − 3𝑥 − 2
16. Find the slope of the tangent line to the graph of 𝑦 = 𝑥 2 + 2𝑥 + 3 at a point
where 𝑥 = 1.
Find the slope of the tangent line to the graph of each equation at 𝑥 = 2.
17. 𝑦 = 𝑥 3
18. 𝑦 = 𝑥 3 − 7𝑥 2 + 4𝑥 + 9
19. 𝑦 = 𝑥 + 1 (𝑥 − 2)
20. 𝑦 = 5𝑥 2 + 7
2
Evaluate each indefinite integral.
21.
𝑥 5 𝑑𝑥
22.
−3𝑥 2 − 𝑥 + 6 𝑑𝑥
Evaluate each definite integral.
23.
7
6𝑥 2 𝑑𝑥
0
24.
4
3𝑥 4 𝑑𝑥
2
25.
2 3
(𝑥
0
26.
1 𝑥 2 −𝑥−2
𝑑𝑥
0 𝑥−2
+ 𝑥 + 1) 𝑑𝑥
27. What information does the derivative of a function tell you?
28. What information does the integral of a function tell you?