NDA 2019 Maths · Mathematics · Continuity and Differentiability · medium

The function f(x)=(1-cos 4x)/(x^2 for x≠0 is made continuous at x=0 by defining f(0) equal to

Single correct option

The function

f(x)=\dfrac{1-\cos4x}{x^2}

for

x\ne0

is made continuous at

x=0

by defining

f(0)

equal to

Show answer and solution

Answer: (B) $8$

We need

f(0)=\lim_{x\to0}\frac{1-\cos4x}{x^2}=\lim\frac{2\sin^22x}{x^2}=2\cdot2^2=8

. Equivalently

\frac12(4)^2=8

using

1-\cos kx\sim\frac{k^2x^2}{2}

. Using

\frac{1-\cos x}{x^2}\to\frac12

without scaling by

k^2

would give

\frac12

, and

16

forgets the factor

\frac12

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake