10. (a) Find T4(x), the 4th degree Taylor polynomial for f(x) = sin x centered at a = π/6. (b) Use Taylor’s inequality to estimate the accuracy of the approximation f(x) ≈ T4(x) when 0 ≤ x ≤ π/3. In

Step-by-step explanation:

By the general expresion:

T4(x) = f(a) + (f'(a)/1!)*(x-a) + (f''(a)/2!)*(x-a)² + (f'''(a)/3!)*(x-a)³ + (f''''(a)/4!)*(x-a)^4

Then:

f(x) = sinx ; f'(x) = cosx ; f''(x) = -sinx ; f'''(x) = -cosx ; f''''(x) = sinx

Since:  sin(π/6) = 1/2 ; cos(π/6) =

Thus, in the expresion for T4(x):

Inequality, by the Taylor's theorem (jpg adjunt):

We need to find M in the interval indicate. Of the analysis from the graf of the function (jpg adjunt), we see a good candidate is:

M = f(π/3) = sin(π/3) =

Then, in the Taylor's theorem:

(a)  

(b)  

Step-by-step explanation:

(a) We have that Taylor's polynomial is given by

In this case we have to compute T4, with a = pi\6. Hence we have to calculate the first derivative until the fourth derivative of f(x):

By replacing we have

(b) the Taylor's inequality is given by

where f(x)<=M, Hence we have

HOPE THIS HELPS!

answer: a. 13/44

step-by-step explanation: judging by the information given to us, we are looking for experimental probability. we can see that 13 males have chosen chocolate ice cream. there are 44 ice creams in total (remember that the total is always the denominator). so our answer is 13/44.

sinn is the total amount of students now and m were the students before, you subtract them both (n-m) and divide that by m. then, since to get a percentage from a fraction you have to multiply by 100, your answer should look like this: n-m/m*100

step-by-step explanation: