MAT321 Exam 2 7 April, 1998
Prof. Thistleton
1. Find the derivatives of the following functions:
(a) f(x) = sin(x)cos(x)
(b) g(x) = 2x+ 1
x−1
(c) h(x) = sin(x3+ 5)
(d) l(x) = x2+ 1
(2x+ 3)2
(e) p(x) = sec(x2)
1
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Practice Exam 2 on Calculus I - Spring 1998 | MAT 151, Exams of Calculus
Material Type: Exam; Professor: Thistleton; Class: Calculus I; Subject: Mathematics; University: SUNY Institute of Technology at Utica-Rome; Term: Spring 1998;
Typology: Exams
Pre 2010
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MAT321 Exam 2 7 April, 1998 Prof. Thistleton
- Find the derivatives of the following functions:
(a) f (x) = sin(x)cos(x)
(b) g(x) =
2 x + 1 x − 1
(c) h(x) = sin(x^3 + 5)
(d) l(x) =
x^2 + 1 (2x + 3)^2
(e) p(x) = sec(x^2 )
- The distance from the origin of an object as a function of time is given by
s(t) = 9 − 6 t^2 + 2t^3
for 0 <= t <= 4.
(a) Find the critical numbers of this function.
(b) When does it reach its maximum distance from the origin?
(c) What is its maximum distance?
(d) When does it reach its minimum distance from the origin?
(e) What is its minimum distance?
- Approximate the value
102 using the method of differentials.
Suppose that the flow rate F , measured in bundles per hour, processed by your plant is modelled by
F =
v 10 + 0. 1 v^2
where v is the speed of the bundles in stations per hour.
(a) What speed will maximize the flow rate at your plant?
(b) What is the maximum flow rate your plant?
- Calculate the following limits.
(a) (^) xlim→∞
x^2 + x − 4 3 x^3 + 5
(b) (^) xlim→∞
2 x − 1 √ 9 x^2 + 1
(c) The surface area of a sphere is given by A = 4πr^2. Using differentials, find the approxi- mate change in area as a sphere expands from r = 20 inches to r = 23 inches.