James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

92 Chapter 2 Limits and Derivatives
1. Explain in your own words what is meant by the equation
lim f sxd − 5
x l 2
Is it possible for this statement to be true and yet f s2d − 3?
Explain.
2. Explain what it means to say that
lim f sxd − 3 and lim f sxd − 7
x l 12 x l1 1
In this situation is it possible that lim x l 1 f sxd exists?
Explain.
3. Explain the meaning of each of the following.
(a) lim f sxd − `
(b) lim f sxd − 2`
x l23 x l 41 4. Use the given graph of f to state the value of each quantity,
if it exists. If it does not exist, explain why.
(a) lim
x l2 2 f sxd
(d) f s2d
y
4
2
(b) lim f sxd
x l 2 1
(e) lim
x l 4 f sxd
(c) lim f sxd
x l 2
(f) f s4d
(j) hs2d
y
(k) lim
x l51hsxd (l) lim hsxd
x l5 2
_4 _2 0 2 4 6 x
7. For the function t whose graph is given, state the value of
each quantity, if it exists. If it does not exist, explain why.
(a) lim tstd
t l 0 2
(d) lim tstd
t l 2 2
(g) ts2d
(b) lim tstd
t l 0 1
(e) lim tstd
t l 2 1
(h) lim tstd
t l 4
y
4
2
(c) lim tstd
t l 0
(f) lim tstd
t l 2
0 x
2 4
2 4
t
5. For the function f whose graph is given, state the value of
each quantity, if it exists. If it does not exist, explain why.
(a) lim
x l 1
f sxd (b) lim x l 3 2
(d) lim f sxd (e) f s3d
x l 3
y
4
(c) lim f sxd
x l 3 1
8. For the function A whose graph is shown, state the following.
(a) lim Asxd
x l23
(c) lim Asxd
x l2 1
(b) lim Asxd
x l2 2
(d) lim Asxd
x l21
(e) The equations of the vertical asymptotes
y
2
0 x
2 4
_3 0 2 5
x
6. For the function h whose graph is given, state the value of
each quantity, if it exists. If it does not exist, explain why.
(a)
(d) hs23d
lim
x l 232hsxd (b) lim
x l 23 1hsxd
(e) lim hsxd
xl0 2
(c) lim hsxd
x l 23
(f) lim hsxd
x l0 1
(g) lim
x l 0
hsxd (h) hs0d (i) lim
x l 2
hsxd
9. For the function f whose graph is shown, state the following.
(a) lim f sxd (b) lim f sxd (c) lim f sxd
x l27 x l23 x l 0
(d) lim
x l 6 2 f sxd
(e) lim f sxd
x l 6 1
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