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# Recitation for Lecture 001 MATH 114

Mason

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This 1 page Study Guide was uploaded by Michale Kuhlman on Monday September 28, 2015. The Study Guide belongs to MATH 114 at George Mason University taught by Staff in Fall. Since its upload, it has received 24 views. For similar materials see /class/215009/math-114-george-mason-university in Mathematics (M) at George Mason University.

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Date Created: 09/28/15

Math 114 Sample Final Exam Questions Spring 2001 14 a Describe how the volume of a threedimensional object is obtained by using the crosssectional area of quotslicesquot and describe how the volume of revolution is obtained when the graph of a function y ag is rotated around the xaxis from m a to m L b Use that method to nd the volume of the solid obtained by rotating the region bounded by y 07 y 3m x 2 and x 10 about the xaxis4 24 a How is the average value of a function de ned by an integral b Find the average value of the function ag x 952 1 on the interval 021 3 Explain how the two differentiation rules known as the product rule and the chain rule are different Then describe how each leads to a result in integration What are these techniques called Give an example of each one 44 Write down the terms that occur when approximating the integral 04 dm when n 8 using either the trapezoid or midpoint rule indicate which you are using Don t simplify at all If you use 16 subdivisions instead what would you expect as the 1 r in the rr 5 a How is the Taylor polynomial of degree n for a function f about a point x a de ned the recipe b Find the Taylor polynomial of degree 2 for 4 7 x2 at a 14 64 What are the two ways an integral is improper How are improper integrals de ned as limits in each case Use the de nition to compute f1 1 dm 74 a What is the difference between a series and a sequence b IF a series is convergent what can you say about the limit of the terms Why c Prove that the geometric series 1 r r2 W 1 117 r 84 a State the integral testr b Explain why it is correct c Use the integral test to show when the pseries E 1 1 m converges and when is diverges based on the value of p

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