GATE2019 CE-1: 4

Question

For a small value of $h$, the Taylor series expansion for $f(x+h)$ is

• A. $f(x)+h{f}’ (x) + \dfrac{h^2}{2!}{f}’’(x) + \dfrac{h^3}{3!}{f}’'’(x)+\dots \infty \\$
• B. $f(x)-h{f}’ (x) + \dfrac{h^2}{2!}{f}’’(x) - \dfrac{h^3}{3!}{f}’'’(x)+ \dots \infty \\$
• C. $f(x)+h{f}’ (x) + \dfrac{h^2}{2}{f}’’(x) + \dfrac{h^3}{3}{f}’'’(x)+ \dots \infty \\$
• D. $f(x)-h{f}’ (x) + \dfrac{h^2}{2}{f}’’(x) - \dfrac{h^3}{3}{f}’'’(x)+ \dots \infty $