# Thread: A quick Taylor series question

1. ## A quick Taylor series question

Suppose you used a Taylor series to evaluate/approximate f(x) with a "x" value.

My question is this - how would you know if the resulting approximation is less or more than the true value of f(x)? Also, am I right in assuming that if the series is alternating, then if the last term is negative then the approximation is less than f(x) and vice versa? But what about non-alternating Taylor series?

Also, on a completely different subject, what are some of the recommended self-study multivariable calculus books? I'm thinking about getting a headstart in multivariable calculus in the summer, so any recommendations?

2. If your approximating series is strictly increasing then your approximation will be less than the exact value. You are always going to be "that error term" less since you are always adding terms. Vice versa if all the terms are negative.

And if you mean the last term included then your assumption is correct.

Hope that helps..

3. Originally Posted by boomlegboom
If your approximating series is strictly increasing then your approximation will be less than the exact value.
Ah, allright. But HOW would I know that it's "strictly increasing" (if there is in fact a way to know...).

4. If it's not alternating and all the terms are positive, every new term adds to the previous term.

5. Ah I see. Thank you very much.