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exam2_fa05

# exam2_fa05 - f satisFes f(0 = 2 and f x = e-7 x 2 ±ind the...

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Name: Section Number: TA Name: Section Time: Math 20A. Midterm Exam 2 November 16, 2005 You may use one page of notes, but no other assistance on this exam. Turn oF and put away your cell phone. Read each question carefully, answer each question completely, and show all of your work. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clari±cation. 1. (6 points) The graph of a function f passes through the point (3 , 1). The line tangent to the graph of f at the point (3 , 1) passes through the point (5 , 7). Find f 0 (3). # Score 1 2 3 4 5 Σ

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2. (6 points) Sylvia is flling spherical balloons with helium For her daughter’s birthday party. The helium valve on the tank releases helium into the balloons at a rate oF 5 cm 3 / sec. When the radius oF a balloon is 2 cm, at what rate is the is the surFace area increasing? Be sure to include the correct units in your answer. The volume V and surFace area A oF a spherical balloon oF radius r are given by V = 4 3 πr 3 and A = 4 πr 2 .
3. (6 points) A certain function

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Unformatted text preview: f satisFes f (0) = 2 and f ( x ) = e-7 x 2 . ±ind the linear approximation for f (0 . 04). 4. (8 points) Let f ( x ) = x + 2 √ x 2 + 2 . Then, f ( x ) =-2( x-1) ( x 2 + 2) 3 2 and f 00 ( x ) = 2(2 x 2-3 x-2) ( x 2 + 2) 5 2 . (a) By evaluating the appropriate limit(s), fnd the horizontal asymptote(s) oF the graph oF f . (b) Determine the interval(s) on which the graph oF f is concave up and the interval(s) on which the graph oF f is concave down. 5. (6 points) Compute the derivatives of the following functions. You need not simplify the resulting expression. (a) (2 points) f ( x ) = e sin(5 x ) (b) (4 points) g ( x ) = ln ( x 4 + 2 x 2 + 1) 3 √ x 2 + 4 ( x 2 + x + 1) 4 ! 6. (6 points) A certain function g satisFes g (1) = 6 and its derivative g satisFes 2 ≤ g ( x ) ≤ 5 for 1 ≤ x ≤ 6. What is the smallest possible value of g (6) and what is the largest possible value of g (6)? Justify your answer and indicate which theorem you used....
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exam2_fa05 - f satisFes f(0 = 2 and f x = e-7 x 2 ±ind the...

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