Question

For the function f(x)=e^(x^(1/2)) , determine the error between the actual function value and the 3rd degree Taylor Polynomial (centered at a = 4) , at x = 4.1

a) 7.57 x 10^-8
b) 1.46 x 10^-8
c) 1.46 x 10^-7
d) 1.46 x 10^-9
e) 7.57 x 10^0

Answer 1

so, the Taylor polynomial at x=4 is

e^√x = e^2 + e^2/4 (x-4) + e^2/64 (x-4)^2 + e^2/1536 (x-4)^3
= 7.5749418520

e^√4.1 = 7.574941837

7.5749418520-7.574941837 = 1.4627*10^-8