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Math · Advanced Math
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EOC 5172- Mathematical Methods in Ut- Homework Assignment 1. Decide which of O, o, or applies best in comparing a. b, C. d, 3x, with x as x→0 tanh x with x as x → 0 sin, x with 1 as x→0 cosx-1 with x as x→0 In x with x as x→00 n! with nn as n → e. 8. withas xo x2 2. Give the first three terms of the Taylor series expansion of the following functions if h and a are small and state the order of the error in terms of h and a if the value of the function in the vicinity of the given values of x and y is approximated by the sum of these three terms: f(x + h) = cos(x + h), where x 0 f(x + h, y + a) = tanh(x + h) cos(y + a) , where x = 0, y = π a. b. exp(y+a) (x+h)1/4,where x= 1.y_1 Expand f(x,y)-cos(x) cos (y) as a Taylor series about x- terms in the expansion to 2nd order in the derivatives of f(x,y) at x = d. /2, y-0, providing π/2, y = 0 3. In Problem 2a, compare your approximations for the given function for h 0.1 and h 0.01 with the exact values of the function at x +h for the given value of x.
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