EXAM 3
Math 131
November 3, 2006
Name
You must show all your work. Partial credit will be given.
1. Find each of the following limits. (9 pts each)
(a) lim
x→0
e2x−1
x
(b) lim
x→∞
x+ 1
x2+ 4x+ 1
(c) lim
x→∞
px2+ 1 −x
(d) lim
x→0xsin 1
x
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9 Questions for Calculus I - Old Examination 3 | MATH 131, Exams of Calculus
Material Type: Exam; Class: Calculus I; Subject: Mathematics; University: Christian Brothers University; Term: Fall 2006;
Typology: Exams
Pre 2010
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EXAM 3
Math 131 November 3, 2006
Name
You must show all your work. Partial credit will be given.
- Find each of the following limits. (9 pts each)
(a) lim x→ 0
e^2 x^ − 1 x
(b) lim x→∞
x + 1 x^2 + 4x + 1
(c) (^) xlim→∞
x^2 + 1 − x
(d) lim x→ 0 x sin
x
- Find the linear approximation of f (x) = sin (3x) at xo = 0. (8 pts)
- Use Newton’s method and xo = 1 to calculate a root of f (x) = x^4 − 3 x^2 + 1. (Accurate to at least 6 decimal places.) (8 pts)
- Find all the positive values of x which cause sin (x) = x^2 −1. (You must use Newton’s method and obtain at least 4 decimals of accuracy.) (8 pts)
- Find all the critical numbers for f (x) = x^3 − 3 x^2 + 3x. (8 pts)
- Find all relative max/min values for the function f (t) = t^2 e−t. (8 pts)
- Suppose f (x) is a function which satisfies all of the following conditions: f (3) = 0, f ′(x) < 0 for x < 0 and x > 3, f ′(x) > 0 for 0 < x < 3, f ′(0) does not exist, (^) xlim→∞ f (x) = 4 and
x→−∞lim f^ (x) =^ ∞^ Sketch a possible graph of this function on the axes below. (8 pts)
1
2
3
4
5
-5 -4 -3 -2 -1 1 2 3 4 5