SI_Practice_Exam_2 - c. 1 / tan 4 (2x) 5. ind the equation...

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Calc 121 Practice Exam 1 Name: Show all of your work and justify your answers completely! You are being graded on the process and well as the answer. Make sure your work is clearly organized and legible. Leave your answers in exact form , this means 2, π and fractions, not crazy decimals. You may leave your answers unsimpliFed . You may not use a calculator. 1. Use the IVT to show that f(x) = 3x 3 – 2x + 10 has a root in [-2, -1]. 2. Write the deFnition of the derivative of f(x) = 1 / (x + 4) at x = 1. Do not simplify your answer or compute the derivative. 3. Use the deFnition of the derivative to show f(x) = (x – 2) 1/3 is not differentiable at x = 2. 4. Compute the following derivatives: a. 2x 3 cos(4x 2 –x) b. (x 3 + 2x) / sin(3x)
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Unformatted text preview: c. 1 / tan 4 (2x) 5. ind the equation of the tangent line. a. f(x) = cos(x) at x = /3 b. 25 = (x 2) 2 + (y + 1) 2 at (6, 2) 6. ind the rate of change of the area of a square with respect the length z of a diagonal. What is the rate when z = 4? 7. A spherical snowball is melting in such a manner that its radius is changing at a constant rate, decreasing from 18cm to 10cm in 20 minutes. How fast is the volume of the snowball changing when the radius is 15cm? 8. Calculate the Taylor Polynomial P 4 (x) to f(x) = sin(x) centered at x = /2 and use this to approximate sin(1.5) 9. Determine where f(x) = cos 2 (x) is increasing/decreasing on [0, 2 ]. ind and classify the local extrema....
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This note was uploaded on 11/16/2011 for the course MUSIC Music 101 taught by Professor Veroni during the Spring '11 term at Antelope Valley College.

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