Let f(x) = 4 + 6x X = We see that the first term does not fit a pattern, but we also see that f() (1) = Hence we see that the Taylor series for f centered at 1 is given by f(x) = 10 + k=1 (x - 1) k. for k ≥ 1.

2. Fill in the table to find the first four terms of the Taylor Series for f(x) = cos(2x) if a = 8 n 0 1 2 3 f(n) (x) f(m) (a) C₁

what is the nth order term in the taylor series expansion of f(x)= exp(x). about x= -3

= √1 + x sin(5x). Note that you may want to find these in a manner other than Find the first four nonzero terms of the Taylor series about 0 for the function f(x) by direct differentiation of the function. √1 + æ sin(5x) =¯++0+0- x +•