Question

Expansion of function f(x) is?

(a) f(0) + ^x⁄1! f^‘ (0) + ^x^2⁄2! f^” (0)…….+^x^n⁄n! f^n (0)

(b) 1 + ^x⁄1! f^‘ (0) + ^x^2⁄2! f^” (0)…….+^x^n⁄n! f^n (0)

(c) f(0) – ^x⁄1! f^‘ (0) + ^x^2⁄2! f^” (0)…….+(-1)^n ^x^n⁄n! f^n (0)

(d) f(1) + ^x⁄1! f^‘ (1) + ^x^2⁄2! f^” (1)…….+^x^n⁄n! f^n (1)

This question was posed to me in an online interview.

I need to ask this question from Taylor Mclaurin Series topic in portion Differential Calculus of Engineering Mathematics

Answer 1

The correct choice is (a) f(0) + ^x⁄1! f^‘ (0) + ^x^2⁄2! f^” (0)…….+^x^n⁄n! f^n (0)

Explanation: By Maclaurin’s series, f(0) + ^x⁄1! f^‘ (0) + ^x^2⁄2! f^” (0)…….+^x^n⁄n! f^n (0)