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Six Questions for Exam II - Calculus I - Fall 2007 | MATH 131, Exams of Calculus

Material Type: Exam; Class: Calculus I; Subject: Mathematics; University: Christian Brothers University; Term: Fall 2007;

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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EXAM 2
Math 131
October 5, 2007
Name
You must show all your work. Partial credit will be given.
1. Find the derivative for each of the following functions. (7 pts each)
(a) f(t) = t53
pt3+ 2
(b) f(x) = x22x
x2+ 5x
(c) f(x) = p4x2+ (8 x2)2
(d) f(x) = sin (x2)
x2
(e) f(x) = (x4
34x)x4
3
x2+ 2
pf3
pf4

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EXAM 2

Math 131 October 5, 2007

Name

You must show all your work. Partial credit will be given.

  1. Find the derivative for each of the following functions. (7 pts each)

(a) f (t) = t^5

t^3 + 2

(b) f (x) =

x^2 − 2 x x^2 + 5x

(c) f (x) =

4 x^2 + (8 − x^2 )^2

(d) f (x) = sin (x^2 ) x^2

(e) f (x) = (x

4 (^3) − 4 x)

x^4 −

x^2

(f) f (x) = etan − (^1) (x)

(g) f (x) = e^2 x^ ln (x^2 + 5)

(h) f (x) = 4x^2 sin (x) sec (3x)

(i) f (x) = sin−^1 (x^3 + 1)

  1. Find all functions g(x) such that g′(x) = f (x) =

x^2 (7 pts)

  1. Prove the x^4 + 6x^2 − 1 = 0 has exactly two solutions. (7 pts)