# Help with Calculus?

##### 1 Answer

May 9, 2018

Use the taylor series for

We now rewrite the inequality.

#0 ≤ 1- x^2/(2!) + x^4/(4!) - 1 + x^2/(2!) ≤ 1/24#

#0 ≤ x^4/(4!) ≤ 1/24#

The maximum of this will be at

If we add more terms it makes no difference.

#0 ≤ x^4/(4!) - x^6/(6!) ≤ 1/24#

The minimum will ALWAYS be

We have therefore proved the required statement.

Hopefully this helps!