Calculus 1 Hour
Exam 2 - Math 221
Fall, 2010
1. |
Find the absolute maximum and minimum and also where these extreme values occur for g(x) = x √(6 – x2 ) Answers: Abs max = 3 at (√3,3) Abs min = - √5 at (-1, √5 ) Also, without using the Mean Value Theorem, show explicitly that the conclusion of this Theorem holds for f(x) = x2 - 4x + 1 on [2,4] . |
2. |
Evaluate the following limits. Hint: Apply l’Hospital’s Rule a. lim ( cos(x) - 3 sin(x) )1/x xŕ0+ b. lim ( ex - e-x ) / sin (3x) Answers: a. e-3 b. 2/3 xŕ0
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3. |
The volume of a cube is decreasing at a rate of 6 cubic inches per minute. At what rate is the surface area changing when the length of the side of the cube is 2 inches? Answer: -12 in2 / minute |
4. |
Consider the following function f(x) with f’(x) and f’’(x) given. f(x) = x / (x2 – 9) , f ’(x) = - (x2 – 9) / (x2 – 9)2 , f ‘’(x) = 2x (x2 + 27) / (x2 – 9)3 Supply the requested information about the graph of y = f(x). You need not justify your answers. types of symmetry if any Answer: symmetric with respect to origin vertical asymptote(s) Answer: x ± 3 horizontal asymptote(s) Answer y = 0 interval(s) of decrease Answers ( - ∞, -3 ), ( -3, 3 ), ( 3, ∞ ) interval(s) of upward concavity Answers ( 3, + ∞ ), ( -3, 0 ) Click here to continue with this exam. |