MTH 141 Applied Calculus
Exam 2 - Chapter 2 (Sections 2.1 to 2.4)
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1. (5 points) Let f (x) = x2 + 5. Use the limit denition to nd the derivatives of f.
Solution:
)
limx0 f (x+xxf (x)
(x+x)2 +5(x2 +5)
limx0
x 2
2
2
x
limx
MTH 141 Applied Calculus
Exam 3 - Chapter 2 (Sections 2.5 to 2.8)
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1. (3 points) Let y = (2x2 5 x + 6)6 . Find f (x) and g (x) such that y = f (g (x).
Solution: f (x) = x6 and g (x) = 2x2 5 x + 6.
2. (3+3+3 points) Find
MTH 141 Applied Calculus
Exam 3 - Chapter 3 (Sections 3.1 to 3.4)
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1. (3 + 4 points) Find the critical numbers and the open intervals on which the function is increasing or
decreasing.
(a) g (x) = x2 2x + 3
Solution: The
MTH 141 Applied Calculus
Exam 3 - Chapter 3 (Sections 3.5 to 3.7)
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1. (3.5 points) Find the number of units x that produces a maximum revenue R, where R = 48x2 0.02x3
Solution:
R = 48x2 0.02x3
R0 = 96x 0.06x2
R00 = 96 0.
MTH 141 Applied Calculus
Exam 1 (Chapter 1) - Fall 2006
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1. (2 + 2 points) Find the x and y intercepts of the following graphs.
(a) y = x2 4x + 3
Solution: To nd the x-intercept, put y = 0. So
x2 4x + 3 = 0
(x 3)(x 1) =
MTH 141 Applied Calculus
Exam 2 - Chapter 2 (Sections 2.1 to 2.4)
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1. (5 points) Let f (x) = 2x 7. Use the limit denition to nd the derivatives of f.
Solution:
f 0 (x) =
=
=
=
=
f (x + x) f (x)
x
2(x + x) 7 (2x 7)
lim
x0
MTH 141 Applied Calculus
Exam 1 (Chapter 1) - Spring 2007
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1. (1.5 + 1.5 + 2 points) Find the domains of the following functions. Write your answer in the interval
form.
(a) f (x) = x2 3x + 4
Solution: f (x) is a polynom
MTH 141 Applied Calculus
Exam 3 - Chapter 2 (Sections 2.5 to 2.7)
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1. (3 points) Let y = (x5 + 7x2 + 3 x3 + 6)8 . Find f (x) and g (x) such that y = f (g (x).
Solution: f (x) = x8 and g (x) = x5 + 7x2 + 3 x3 + 6.
2. (3+3
MTH 141 Applied Calculus
Exam 3 - Chapter 3 (Sections 3.1 to 3.4)
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_
1. (3 + 4 points) Find the critical numbers and the open intervals on which the function is increasing or
decreasing.
(a) g (x) = x2 + 3x 9
Solution: The
MTH 141 Applied Calculus
Exam 3 - Chapter 3 (Sections 3.5 to 3.7)
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_
1. (4.5 points) Find the number of units x that produces a maximum revenue R, where R = 400x x2
Solution:
R = 400x x2
R0 = 400 2x
R00 = 2
So
R0 = 0
400