Find the remainder in the Taylor series centered at the point a for the following function. Then show that limn→[infinity]Rn(x)=0 for all x in the interval of convergence. f(x)=cos x, a= π/2

Step-by-step explanation:

From the given question; the objective is to show that :

for all x in the interval of convergence f(x)=cos x, a= π/2

Assuming for the convergence f the taylor's series , f happens to be the derivative on an open interval I with a . Then the Taylor series for the convergence of f , for all x in I , if and only if    

where;

is a remainder at x and c happens to be between x and a.

Given that:

a= π/2

Then; the above equation can be written as:

so c now happens to be the points between π/2 and x

If we recall; we know that:

(as a result of the value of n)

However, it is true that for all cases that  

Hence, the remainder terms is :

If   for all x and x is fixed, Then

answer: y = -2.5x - 15

              (-6,0)

step-by-step explanation:

the answer is 40.

proof: