Spring 2024
Test 1
Math 1041
Department of Mathematics
Temple University
23 February 2024
Name:
Instructor/Section:
Question Out of Points
This exam consists of 12 questions.
1 13
You have 90 minutes to complete 2 12
the entire test.
3 12
You are NOT permitted to use a 4 9
calculator on any portion of this test.
5 6
Show all relevant work. 6 5
No work, no credit.
7 9
Good Luck! 8 6
9 8
10 9
11 8
12 8
Total 105
, 13pt 1. Use the graph of the function f (x) shown at right to answer the following.
Part I: State the values of the following limits. If the limit is infinite, please state whether
it is “∞” or “−∞”. If the limit does not exist (and is not infinite), state “DNE” and explain
why it does not exist.
(a) lim f (x)
x→−2−
(b) lim f (x)
x→−2+
(c) lim f (x). Justify your answer.
x→−2
1
(d) lim+ . Justify your answer.
x→3 f (x)
(e) lim (4x2 − f (x)). Use limit laws to justify your answer.
x→1
Part II:
(a) State all number(s) a at which f is discontinuous but is continuous from the left.
a=
(b) State the number(s) b at which f has removable discontinuity. How would you define f (b) in
order to make f continuous at b?
b= f (b) =
(c) State all number(s) c at which the function is continuous but is not differentiable.
c=
Test 1
Math 1041
Department of Mathematics
Temple University
23 February 2024
Name:
Instructor/Section:
Question Out of Points
This exam consists of 12 questions.
1 13
You have 90 minutes to complete 2 12
the entire test.
3 12
You are NOT permitted to use a 4 9
calculator on any portion of this test.
5 6
Show all relevant work. 6 5
No work, no credit.
7 9
Good Luck! 8 6
9 8
10 9
11 8
12 8
Total 105
, 13pt 1. Use the graph of the function f (x) shown at right to answer the following.
Part I: State the values of the following limits. If the limit is infinite, please state whether
it is “∞” or “−∞”. If the limit does not exist (and is not infinite), state “DNE” and explain
why it does not exist.
(a) lim f (x)
x→−2−
(b) lim f (x)
x→−2+
(c) lim f (x). Justify your answer.
x→−2
1
(d) lim+ . Justify your answer.
x→3 f (x)
(e) lim (4x2 − f (x)). Use limit laws to justify your answer.
x→1
Part II:
(a) State all number(s) a at which f is discontinuous but is continuous from the left.
a=
(b) State the number(s) b at which f has removable discontinuity. How would you define f (b) in
order to make f continuous at b?
b= f (b) =
(c) State all number(s) c at which the function is continuous but is not differentiable.
c=
