math 1720 final
.pdf
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School
University of Windsor *
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Course
1720
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
10
Uploaded by UltraSeaLionMaster403
UNIVERSITY OF WINDSOR
DEPARTMENT OF MATHEMATICS AND STATISTICS
Di
ff
erential Calculus MATH 1720/1760
Final Exam
Wednesday, December 15, 2021, 12:00 pm - 2:30 pm
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:
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all
questions.
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.
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2
1.
(17)
Evaluate the following limits:
(a) lim
x
→
0
x
+ tan
x
3
x
+ 4
x
2
(b) lim
x
→
7
-
x
2
-
5
x
-
14
x
2
-
49
(Do not use L’Hospital rule in part(b))
(c) lim
x
→∞
e
-
3 sin
x
x
2
(d) lim
x
→
1
+
sin(
π
x
) ln (
x
-
1)
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3
2.
(5)
For what value(s) of the constant
c
is the function
f
continuous on (
-∞
,
∞
)
f
(
x
) =
c
2
-
(
x
+ 1)
c,
if
x >
1
(2
x
+ 1)
c
-
x
2
-
5
,
if
x
≤
1
3.
(6)
Use the definition of derivative to find the derivative of
f
(
x
) =
√
3
x
-
7
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4
4.
(9)
Consider the equation
e
x
+ 2
x
= 0
(a) Use the Intermediate Value Theorem to show that the equation has at least one real root.
(b) Use Rolle’s theorem to show that the equation has at most one real root.
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