AP Calculus AB
sin 5x
x→0 cos 4x
1. lim
sin2 3x
x→0 x2 cos x
2. lim
sin 5x
1
x→0
sin x
3
x
4. lim
x→0 tan x
3. lim
1 + sin x
5. lim
π 1 − cos x
x→
2
cos 2x
x→∞
x2
6. lim
Worksheet 7
4x3 − 32
x→2 5x2 − 20
11. lim
5
x→4 x − 4
x
4
13. lim sin
x→0 x
5
12. lim−
14. Find the domain and range of the function
√
f (x) = x2 − 9 + 1
4x3 − 5
x→1 5x2 − 6
15. lim
16. lim+
x→2
6x3 − 5x
7. lim 2
x→∞ x + 4x3
4a2 − x2
x→b 2a + x
8. lim
8x3 − 5x
9. lim
x→−∞ x2 − 3x
x2 + x4
x→∞ x2 + x6
10. lim
2x − 2
x−4
8x2 − 2x3
x→−∞ 2x2 − 4x




x2 − 4,




18. Graph f (x) = x + 3,






−x + 2,
17. lim
x ≤ −3
−3 < x < 2
x≥2
19-23: Use the graph of f (x) to answer the questions
19. lim+ f (x)
x→1
20. lim− f (x)
x→1
21. lim f (x)
x→1
22. lim f (x)
x→−1
23. lim f (x)
x→2
24-26: Use the graph of g(x) to answer the questions
24. Use the 3-part definition of continuity to show if
g(x) is continuous at x = 3
25. What kinds of discontinuities are shown in the
graph of g(x)
26. Is there a removable discontinuity? If so, assign a
value to remove it.
27. If f (x) =



2x − 1,
x≤1
, use the definition of continuity to show if f (x) is continuous at x = 1


−3x + 1, x > 1

2

 x + 6x + 8 , x 6= −2

x+2
28. If f (x) =
, use the definition of cont. to show if f (x) is continuous at x = −2


2,
x = −2
x3 + 8
, use the definition of continuity to show if f (x) is continuous at x = −2
29. If f (x) =
x+2
x3 − 64
, then f (x) has a point discontinuity. Assign a value to f (x) that removes this
x−4
discontinuity
30. If f (x) =
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