Re: Taylor Series Problem

A **terms** of the Taylor Series are those that are being added.

The "general term" is , so say exactly what that is for this f and c, in terms of n.

The "first three terms" are:

(but numerically computed from f and c),

(but numerically computed from f and c),

(but numerically computed from f and c).

However, those might not be the first three **non-zero** terms.

The answer wants those f and c references replaced with values as determined by what's given for f and c.

For instance, the first term is:

The second term is:

(Notice that this is NOT a "non-zero term").

The 3rd term is:

Re: Taylor Series Problem

Use the definition of the taylor series.Compute the derivatives of sin2x at pi/4 until you have 3 nonzero derivativs.Try to figure out the general form and write the general element of the series.

Re: Taylor Series Problem

Quote:

Originally Posted by

**johnsomeone** A "term" of the Taylor Series

are those

that are being added.

The "general term" is

, so say exactly what that is for this f and c, in terms of n.

The "first three terms" are:

(but numerically computed from f and c),

(but numerically computed from f and c),

(but numerically computed from f and c).

However, those might not be the first three

**non-zero** terms.

The answer wants those f and c references replaced with values as determined by what's given for f and c.

For instance, the first term is:

The second term is:

The 3rd term is:

When it says "non-zero terms" is it wanting (f^n(c)/n!)(x-c)^n when it doesn't equal 0 when you plug in f and c?

Re: Taylor Series Problem

Correct. It's the first 3 terms (starting with n=0), such that when you plug in for f and c, that the term isn't zero. I've already done the first two for you.

The first two non-zero terms are:

You now need only find the 3rd non-zero term.

Re: Taylor Series Problem

just the coefficient.(x-c)^n is clearly 0 at c.