find the nth taylor polynomial centered at x0 for fxsinh9xSo

find the nth taylor polynomial centered at x=0 for f(x)=sinh(9x)

Solution

similarly above question cal solve

they want you to generate a taylor polynomial like:
http://upload.wikimedia.org/math/0/1/4/0…
where the f^(n)(a) is the nth derivative of f(x) taken at \'a\'

if you wanted to expand the answer, it would be something like this:
T(x) = 1 - 2(x-1) + 3(x-1)^2 - 4(x-1)^3 + 5(x-1)^4... (etc)

the taylor polynomial is a very accurate way to estimate f(a) with just paper and pencil (as an extreme example)