How do you find the coefficients of the Taylor series for f centered at a?

Solution 3EStep 1:General expression of Taylor series of a function f(x) centered at ‘a’ is ; f(a) +(x-a) +++.............We have the formula to find the coefficients of Taylor series of the function f centered at ‘a’.We calculate the coefficients , i = 0,1,2,3……….in Taylor series of the function f centered at ‘a’ As, = , for k = 0,1,2 Example ; The coefficients of the Taylor series for f(x) = centered at a =0 is;We know that the Taylor series of centered at a = ‘0’ is; = +++...........Consider , f(x) = , then f(0) = =1 , then , then , then ……………………………..Therefore , the coefficients of Taylor series of centered at a = ‘0’ are; = , then = = =1 = = =1, = = , = = ……….Therefore , coefficients are ; 1,1 , , and ………...