Quiz Prep: Math Analysis
Limits: Sections 1.1 – 1.3
Use the calculator to view the function’s graph and/or its table, and estimate the following limits.
1. h(x) = x2 – 5x
3. f(x) = x cos x
4. f(t) = t|t – 4|
12( x  3)
2. g ( x) 
x9
a) lim h( x )
a) lim g ( x)
a) lim f ( x)
a) lim f (t )
b) lim g ( x)
b) lim f ( x)
b) lim f (t )
Find each limit.
5. lim x 2
6. lim (3x  2)
7. lim(2 x  1)
8. lim( x 2  1)
9. lim( x 2  x  2)
10. lim(3x 3  2 x 2  4)
11. lim x  1
12. lim 3 x  4
13. lim ( x  3) 2
14. lim(2 x  3) 3
x 5
b) lim h( x)
x 1
x4
x2
x  4
x2 1
x 1
x
17. lim
21. lim cos x
x 1
25.
lim sin x
x  5 / 6
x / 3
x0
x 3
x 4
x 1
x 3
x 3
1
x 2 x
x 1
x 4
2
x 3 x  2
16. lim
x 1
x4
19. lim sin x
20. lim tan x
x
23. lim sec 2 x
24. lim cos 3x
22. lim sin
x 1
26.
x 0
t 1
15. lim
x 0
18. lim
t 4
x0
2
lim cos x
x  5 / 3
x  / 2
x 0
27. lim tan
x 3
x
4
x 
x 
 x 
28. lim sec 
x 7
 6
Use the information to evaluate the limits.
29. Given: lim f ( x)  2 and lim g ( x)  3
30. Given: lim f ( x) 
a) lim[5g ( x)]
a) lim[ 4 f ( x)]
b) lim[ f ( x )  g ( x )]
b) lim[ f ( x )  g ( x )]
c) lim[ f ( x) g ( x)]
c) lim[ f ( x) g ( x)]
x c
xc
x c
and lim g ( x) 
x c
1
2
x c
xc
xc
f ( x)
xc g ( x )
31. Given: lim f ( x)  4
f ( x)
xc g ( x )
32. Given: lim f ( x )  27
d) lim
d) lim
x c
x c
3
a) lim[ f ( x)]
a) lim 3 f ( x)
xc
xc
3
2
x c
xc
b) lim
x c
xc
b) lim
f ( x)
x c
f ( x)
18
c) lim[3 f ( x)]
c) lim[ f ( x)]2
d) lim[ f ( x)]3 / 2
d) lim[ f ( x)]2 / 3
x c
xc
xc
xc
Use the graph to determine the limit, if it exists. When possible, reduce the original function.
x
 2x 2  x
x3  x
x 2  3x
36. f ( x)  2
33. g ( x) 
34. h( x) 
35. g ( x) 
x x
x
x 1
x
a) lim g ( x)
a) lim h( x)
a) lim g ( x)
a) lim f ( x)
b) lim g ( x)
b) lim h( x )
b) lim g ( x)
b) lim f ( x)
x0
x 1
x 2
x 0
x1
x 1
x1
x0
Find the limit of the function, if it exists. When possible, reduce the original function.
2x 2  x  3
x2 1
37. lim
38. lim
x  1
x 1 x  1
x 1
x3  8
x  2 x  2
39. lim
x3  1
x  1 x  1
40. lim