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Unformatted text preview: Chapter 12 Approximation methods 12.1 An approximation for the square root Use a linear approximation to find a rough estimate of the following functions at the indicated points. (a) y = x at x = 10. (Use the fact that 9 = 3.) (b) y = 5 x 2 at x = 1. (c) y = sin( x ) at x = 0 . 1 and at x = + 0 . 1 12.2 Use the method of linear approximation to find the cube root of (a) 0 . 065 (Hint: 3 . 064 = 0 . 4) (b) 215 (Hint: 3 216 = 6) 12.3 Use the data in the graph in Figure 12.1 to make the best approximation you can to f (2 . 01). 12.4 Using linear approximation, find the value of (a) tan44 , given tan 45 = 1, sec 45 = 2, and 1 . 01745 radians. (b) sin 61 , given sin 60 = 3 2 , cos 60 = 1 2 and 1 . 01745 radians. v.2005.1  September 4, 2009 1 Math 102 Problems Chapter 12 (2, 1) (3, 0) y = f(x) Figure 12.1: Figure for Problem 12.3 12.5 Approximate the value of f ( x ) = x 3 2 x 2 + 3 x 5 at x = 1 . 001 using the method of linear approximation. 12.6 Use linear approximation to show that the each function below can be approximated by the given expression when  x  is small (i.e. when x is close to 0). (a) sin x x (b) e x 1 + x (c) ln(1 + x ) x 12.7 Approximate the volume of a cube whose length of each side is 10 . 1 cm. 12.8 Finding critical points Use Newtons method to find critical points of the function y = e x 2 x 2 12.9 Estimating a square root Use Newtons method to find an approximate value for 8. (Hint: First think of a function, f ( x ), such that f ( x ) = 0 has the solution x = 8)....
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This note was uploaded on 05/19/2011 for the course MATH 102 Math 102 taught by Professor Allard during the Winter '09 term at The University of British Columbia.
 Winter '09
 Allard

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