Question

FIND THE TAYLOR sEtuEs ExpAMson ron f ABovt x=a

A f(x)= x / 1 a=3
B f(x)=cosx a=1
C f(x)=sin(πx) a=1

Answer 1

The Taylor series expansion for a function f(x) can be found by calculating its derivatives up to the desired order and substituting the values of x and a into the expansion formula.

Step-by-step explanation:

The Taylor series expansion for the function f(x) = x at x = a is given by:

f(x) = f(a) + f'(a)(x - a) + f''(a)(x - a)^2/2! + f'''(a)(x - a)^3/3! + ...

For the given functions:

1. f(x) = x / (1 + a), a = 3
2. f(x) = cos(x), a = 1
3. f(x) = sin(πx), a = 1

To find the Taylor series expansion for each function, we need to calculate the derivatives of the functions up to the desired order and substitute the values of x and a into the expansion formula.