And, you can also show either by inspection if you like that there

are seven terms here.

N is equal to 7 and just convince yourselves that the last expression is

indeed given by this expression l is equal to r to the n minus 1.

Now we'll finish with an example on the Taylor series and

we want to form a Taylor series of the function f of x equals exponential or

E to the 2x about the origin about a equals 0,

to estimate the value of the function at point B, which is close to A.

And the question is,

what are the first two terms in the expansion about X equals 0?

Which of these alternatives?

So, here is the section again from the reference handbook.

And, here is the formula for the Taylor series.

F of X is equal to function evaluated at A plus the first derivative

F prime evaluated at A divided by 1 factorial times X minus A.

Plus the second derivative F double prime evaluated at A divided

by 2 factorial multiplied by X minus A squared, etcetera.

But here, we're asked only for the first two terms, so

we just want to evaluate these terms in the expansion.