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Calculus Ch. 1 NAME____________________
Chapter Review
Find each limit analytically. All limits must be justified.
2
x 2
3x 4 lim โ x 2
2
x 2
x 3, x 2 lim f x if f x โ x 5, x 2
๏ฃณ โ^ >
x 1
x lim cos 2
โ
2
x 1 2
2x 1, x 1 lim f x if f x 2x , x 1 โโ
2
x 2
x x 2 lim โโ x 2
2
x 3
x x 12 lim โ 3 x
x 2
x 2 lim โ x 2
x 3
x 3 lim โโ x 3
x 0
x 4 2 lim โ x
x 0
sin 2x lim โ x
3
x 0
sin x lim โ x
x
1 cos x lim โ ฯ x
x 1
lim 3x 2 โ โ
x 3
lim 4x 5 โ โ
x 2 2
x lim x 4 โ + โ
x 4
3x 12 lim x 4 โโ
x 5
2x 10 lim 5 x โโ
x 4 2
lim โ (^) x โ 8x + 16
19. Find ( ) ( ) ( ) ( )
x c x c x c
lim f x g x if lim f x and lim g x โ โ 3 โ 5
20. Using the information from example 19, find { ( ) ( )}
x c
lim 5 f x g x โ
When are the following functions discontinuous? Identify each discontinuity removable or
non-removable. Justify all work.
2
x 3 f x x x 6
f g(x) if f x and g x x 1 x 1
For which value is f(x) not continuous? Identify each discontinuity removable or non-
removable. Justify all work.
2
3x 2, x 0 f x if f x x 1, x 0
๏ฃฑ^ +^ โค
๏ฃณ โ^ >
2x 3, x 1 f x if f x x 2, x 1
๏ฃฑ^ +^ โค โ
๏ฃณ +^ > โ
Find the vertical asymptotes, if any.
x 3 f x 2x 1
2
x 3 f x x 9
2
x 4 f x x 16
Is the following true or false?
32. If the value of ( ) ( )
x c
f c 5 then the lim f x 5. โ
- Use the graph to determine the limit for each of the following.
a) 0
lim x โ
= _________ b) 7
lim x โโ+
=__________
c) 7
lim x โ
=__________ d) 1
lim x โโโ
=___________
e) 4
lim x โโ
=__________ f) 8
lim x โโ+
=___________
g) 8
lim x โโ
=__________ h) 1
lim x โโ
=___________
- rem @ x = 3, non-rem @ x = โ 2 26. non-rem @ x = 0 27. non-rem @ x = 0
- none 29.
x 2
= โ 30. x = 3 31. none
- False
- a) 8 b) 6 c) DNE d) โโ e) 1 f) โโ
g) DNE h) โโ
