Find t5(x) : taylor polynomial of degree 5 of the function f(x)=cos(x) at a=0 . (you need to enter function.) t5(x)= find all values of x for which this opproximation is within 0 < =|| x.002652 of the right answer.

The polynomial is an approximation with an error less than or equals to 0.002652 for x in the interval

[-1.113826815, 1.113826815]

Step-by-step explanation:

According to Taylor's theorem

with

for some c in the interval (-x, x)

In the particular case f

f(x)=cos(x)

we have

therefore

and the polynomial approximation of T5(x) of cos(x) would be

In order to find all the values of x for which this approximation is within 0.002652 of the right answer, we notice that

for some c in (-x,x). So

and we must find the values of x for which

Working this inequality out, we find

Therefore the polynomial is an approximation with an error less than or equals to 0.002652 for x in the interval

[-1.113826815, 1.113826815]

the answer is d

step-by-step explanation: