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Math 1105 Winter 2012/2013 Assignment 5 Due Feb 14 at 2:30 pm In this lab we will use derivatives to approximate small changes in dierentiable functions. You have learned that for small changes in x y f0(x)x (1) Let f(x) = xex: We will use this to approximate f(1:01): 1. Calculate f0(x). Calculate f0(1): 2. We know f0(1). What will the value for x be? Now use the formula above to approximate y and use this to approximate f(1:01): 3. The value of x increasing from 1 to 1:01 is an percentage increase of 1%: What is the approximate percentage increase of f(x) increasing from f(1) to f(1:01)? 4. Use your calculator to calculate f(1:01) exactly. How large is our error (the dierence between our approximate and exact solution)? 5. Using the method above approximate the percentage increase of area of a regular hexagon if the length of each side is increased by 2%. You will have to look up the formula for the area of a regular hexagon. Homework Problems Section 3.1 (p169) # 10 Section 3.3 (p181{182) # 30 40 66 Section 3.5 (p197{198) # 16 28 32 Section 4.3 (p232) # 8 18 24 30 1

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