Math1210 Weekly Assignment 2
Spring, 2016
(Limits 1.1, 1.3, 1.4)
instructor:
Uid number:
name:
Instructions: Please show all of your work as partial credit will be given where appropriate,
and there may be no credit given for problems where there is no work shown. All answers
should be completely simplified, unless otherwise stated. No calculators or electronics of
any kind are allowed. (Total of 50 points possible.)
1. (15 points) Evaluate the following limits
x2 − 2x + 2
x→0 2x3 + 5x + 1
(a) (5 points) lim
Answer:
3
(b) (5 points) lim
x→−2 x2
x +8
− 2x + 4
Answer:
x2 − 16
(c) (5 points) lim √
x→4
x−2
Answer:
2. (15 points) Evaluate each limit.
(a) (5 points) lim θ cos θ
θ→π/2
Answer:
1 − cos2 θ
θ→0
θ2
(b) (5 points) lim
Answer:
sin2 (3t)
t→0
4t2
(c) (5 points) lim
Answer:
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3. (8 points) For this graph of y = f (x), answer the following questions. Write DNE if the
limit or function value does not exist.
(a) lim f (x) =
(e) f (2) =
x→0
(b) lim− f (x) =
(f) f (0) =
(c) lim+ f (x) =
(g) f (π) =
x→2
x→2
(d) lim f (x) =
x→2
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4. (12 points) Define a piecewise function (algebraically) whose domain is all real numbers
and that has the following properties. Also, draw its graph on the xy-plane below.
(a) lim+ f (x) = 3
x→1
(b) lim− f (x) = 5
x→1
(c) lim f (x) = 2
x→−2
(d) f (−2) = −1
Function definition:
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