Practice Test 3a

# Practice Test 3a - ln(5 b Find the intersection of this tangent line with the x axis III(20 points At what rate is the volume of a sphere changing

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Prep Test IIIA for Calculus I, Math 1501C1, October 21, 2002 Name: This test is to be taken without calculators and notes of any sorts. The allowed time is 50 minutes. Write answers in boxes where provided. Provide exact answers; not decimal approximations! For example, if you mean 2 do not write 1 . 414 . . . .

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I: (20 points) Compute the derivatives of the functions a ) ln(1 + x 2 ) b ) arcsin(4 x 2 ) c ) cos(sin( x 2 )) d ) x 2 1 + cos( x 2 ) e) For f ( x ) a di±erentiable function, calculate the derivative of (1 - x ) 2 f ( x ) at x = 1.
II: (20 points) a) Find the equation of the tangent line to the graph of the function f ( x ) = ln(1 + x 2 ) at the point (2

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Unformatted text preview: , ln(5)). b) Find the intersection of this tangent line with the x axis. III: (20 points) At what rate is the volume of a sphere changing at the instant when the surface area is increasing at the rate of 4 square centimeters per minute and the radius is increasing at the rate of 0.1 centimeter per minute? IV: (20 points) Find the minimum of the expression a ln( a ) + b ln( b ) among all positive numbers a, b > 0 with a + b = 1. V: (20 points) b) How many roots can the equation x 6 + 6 x 2 + x + 1 = 0 at most have?...
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## This note was uploaded on 02/07/2011 for the course MATH 1501 taught by Professor N/a during the Fall '08 term at Georgia Institute of Technology.

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Practice Test 3a - ln(5 b Find the intersection of this tangent line with the x axis III(20 points At what rate is the volume of a sphere changing

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