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Unformatted text preview: Review Exercises for Final, Calculus 1A Instructor: Zvezdelina Stankova Problem 1. Consider the graph of f ( t ) in #2, p.387. Let g ( x ) = integraldisplay x f ( t ) dt . (a) On what intervals is g ( x ) increasing? Why? (b) On what intervals is g ( x ) concave up? Why? (c) Calculate the 7th midpoint approximation M 7 of g (7). (d) Calculate the exact value of g (5). Problem 2. Let y ( x ) = integraldisplay x 2 2 16 +1 tan x 1 2 + t 4 dt . Find lim x 4 y ( x ) and y ( 4 ). Explain. Problem 3. A body moves along a straight line with acceleration a ( t ) = 2 t + 3 m/sec 2 . The velocity at time t = 0 is v (0) =- 4 m/sec . (a) Find the velocity and the speed functions for the time period- 3 t 10. Draw their graphs. (b) Find the average speed for the time period [- 3 sec, 10 sec ]. (c) Find the displacement of the body at time t = 10 sec relative to the position at t =- 3 sec ....
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This note was uploaded on 03/30/2010 for the course MATH 11111 taught by Professor Stankova during the Fall '09 term at University of California, Berkeley.
- Fall '09