Limits Evaluate the following limits using Taylor series.

Solution 16E

Step 1:

In this problem we have to evaluate using taylor series.

We know the taylor series of ln(x) , centered at 1 is ;

ln(x) = (x-1) -

Consider , =

=

= , since cancel out the like terms.

= , since , then (x-1) = 0

=

=

= 1.

Therefore , = 1.