Question

The necessary condition for the Maclaurin's expansion to be true for f(x) is…...

Answer 1

Answer: the correct answer is D

Step-by-step explanation:

: By Maclaurin’s series, f(0) + x⁄1! f‘ (0) + x2⁄2! f” (0)…….+xn⁄n! fn (0)

where, f(x) should be continuous and differentiable upto nth derivative.

Answer 2

Answer:

The function f(x) should be continuous and differentiable

Step-by-step explanation:

Maclaurin's expansion is given by

$f(x) = f(0)+f^{'}(0)x + \frac{f^{''}(0) }{2!} x^{2} + .....+\frac{f^{k}(0) }{k!}x^{k} + ....$

Here every term in the expansion is the derivative of the function f(x), therefore function f(x) should be continuous and differentiable up to the nth derivative

Hence the necessary condition for the  Maclaurin's expansion to be true for f(x) is should be continuous and differentiable