Consider the problem of accurately eval- uating f(x)=e-1 for x 0 (say, |x| < 10-6). a)...

 

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Consider the problem of accurately eval- uating f(x)=e-1 for x 0 (say, |x| < 10-6). a) Use a Taylor series to find a degree-3 polynomial approximation to f(x). Use big-O notation to describe the remainder. b) For 0, is the relative condition number of f(x) large or small? c) If you implement the function in MATLAB as f = @(x) exp(x)-1, why might your implementation not be as accurate as you would like? Consider the problem of accurately eval- uating f(x)=e-1 for x 0 (say, |x| < 10-6). a) Use a Taylor series to find a degree-3 polynomial approximation to f(x). Use big-O notation to describe the remainder. b) For 0, is the relative condition number of f(x) large or small? c) If you implement the function in MATLAB as f = @(x) exp(x)-1, why might your implementation not be as accurate as you would like?

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a For the function fx ex for x 0 we can use the Taylor series expansion of ex around x 0 to find a d... View the full answer