Calculating Limits Exercises
STUDYSmarter
Question 1
Calculate each of the following limits, if they exist. If they don’t exist, give your
reasoning.
x2 − 2x − 3
x→3
x+1
(a) lim 3x2 + 4x − 3
x→4
(k) lim
2x + 1
x→5 2 − x
(l) lim
x+4
x→−2 x − 4
(b) lim
x2 − 16
x→4
2x
x2 + 4
(m) lim
x→−1 x + 1
(c) lim
1
x→0 x
x2 + x − 12
x→−4
x2 − 16
√
(o) lim 19 − x
(d) lim
(n) lim
2
x→3 x − 3
(e) lim
x→19
2
(f ) lim
x→3
x −9
x−3
x2 + x
x→−1 −2x
(p) lim
(g) lim x2 + x + x3
x+1
x→1 x2 + 1
(q) lim
x→−1
(h) lim 2x + 5
x3 − 2
x→2 x − 2
x→0
(r) lim
25 − x2
x→−5 5 + x
(i) lim
(s) lim
x→−3
x2 + x − 2
x→1
x−1
(j) lim
G Coates
x−3
x−3
4 − x2
x→−2 2 − x
(t) lim
1
Dec 2016
Calculating Limits Exercises
STUDYSmarter
Question 2
Calculate each of the following limits, if they exist. If they don’t exist, give your
reasoning.
x2 + 3x + 9
x→∞ x2 − 7x − 16
(g) lim
12x + x2 + 4x3
x→∞ 2 − x3 + 4x2
4x3 + 6x − 6
x→∞
2x2 + 9
(h) lim
2x3 + 2x + 6
x→∞ 4x2 + 5x − 9
(i) lim
(d) lim
4x7 + 2
x→−∞ 3x5 − 9x2
(j) lim
2x10 − 5x7 + 2x
(e) lim
x→∞
2x11 + 3x
(k) lim
(a) lim
1+x
x→∞ 1 + x4
(b) lim
x5 − 1
x→−∞ 1 − x3
(c) lim
2x2 + 3x − 7
x→∞ 9x2 − 4x + 18
2x7 + 5
x→∞ x − 9
7 − x4
x→∞ 3 − 9x2 + 8x8
1 − 3x2
x→−∞ 4x − x2
(l) lim
(f ) lim
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Dec 2016
Calculating Limits Exercises
STUDYSmarter
Solutions
Question 1
(a)
61
− 11
3
(c)
0
(d)
DNE (diverges to ∞)
(e)
DNE (diverges to ∞)
(f )
6
(g)
−1
(i)
10
(k)
0
(l)
− 13
(n)
7
8
(p)
0
(t)
0
(c)
DNE (diverges to ∞)
(f )
3
(j)
2
9
(b)
(j)
3
(m) DNE (diverges to ∞)
(o)
DNE (Right-hand limit DNE)
(r)
DNE (diverges to ∞)
(s)
1
(h)
5
(q)
1
Question 2
(b)
DNE (diverges to ∞)
(a)
1
(d)
DNE (diverges to ∞)
(h)
0
(k)
DNE (diverges to ∞)
(i)
(e)
0
DNE (diverges to ∞)
(l)
(g)
−4
0
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G Coates
3
Dec 2016