Answer to Question #156956 in Civil and Environmental Engineering for Ian

Question

Expand the function using Taylor Series Expansion (first 8 terms).

1. e^x, a=2

Answer 1

he function is given as

f(x)=e^x

the successive deriviatives of the function f(x) are given as

f¹(x)=e^x,, f²(x)=e^x,, f³(x)=e^x,,

f⁴(x)=e^x,, f⁴(x)=e^x,, f⁶(x)=e^x,,

f⁷(x)=e^x,, f⁸(x)=e^x

^{the value of the function and it der.. at the point a=2 are}

f¹(x)=e² f²(x)=e² f³(x)=e²

f⁴(x)=e² f⁵(x)=e² f⁶(x)=e²

f⁷(x)=e² f⁸(x)=e²

the taylor polynomial of degree n approximating the function f(x) from n x= a is given by

f(x)=f(a)+f1(a)(x-a)+F2(A)/2!(X-a) ²