Use Taylor plynomial approximations to avoid loss of significance errors when x is near 0;

((e^x) - 1)) / x

and

(x + log(1-x)) / x^2

Any advice...not sure how to go about this. Thanks.

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- Sep 18th 2009, 10:11 PMjzelltTaylor Polynomial
Use Taylor plynomial approximations to avoid loss of significance errors when x is near 0;

((e^x) - 1)) / x

and

(x + log(1-x)) / x^2

Any advice...not sure how to go about this. Thanks. - Sep 18th 2009, 10:18 PMxxlvh
For (e^x-1) / x, is x the exponent or x - 1? I just wanted to double check that, anyways, I had a question I believe to be identical to this one on my calc final last year..

If it is only x, then to solve this, use the Taylor Polynomial for e^x centered at x = 0 which you should have memorized, then subtract one from it and then divide every term by x.