MATH 1210: Homework §1.1
due June 11, 2013
Instructions: Do the following problems. Show all of your work.
In Problems 1 − 17, find the indicated limit. You may need to do some algebra first.
1. lim (x − 5)
x→3
3. lim (x2 + 2x − 1)
x→−2
5. lim (t2 − 1)
t→−1
x2 − 4
x→2 x − 2
7. lim
x3 − 4x + x + 6
x→−1
x1
9. lim
1
x2 − t2
x→−t x + t
11. lim
p
(t + 4)(t − 2)4
t→2
(3t − 6)2
13. lim
x4 − 18x2 + 81
x→3
(x − 3)2
15. lim
(2 + h)2 − 4
h→0
h
17. lim
Do the following
33. Sketch the graph of


−x
f (x) = x


1+x
if x < 0
if 0 ≤ x < 1
if x ≥ 1
Then find each of the following or state that it does not exist
2
(a) lim f (x)
x→0
(b) lim f (x)
x→1
(c) f (1)
(d) lim f (x)
x→1+
38. Evaluate
√
lim
x→1
x+2−
x
√
2
Hint: Rationalize the numerator by multiplying the numerator and denominator by
√
2.
3
√
x + 2+