If the function f(x)=( ( x)- ( x))/( x- x) is continuous at x=0 , then f(0) is equal to ________

Correct answer: 0 _ x arrow 0 (( ( x)- x)/( ^3 x) ( ^3 x)/(x^3)+( x- x)/(x^3)+( x- ( x))/( ^3 x) ( ^3 x)/(x^3))/(( x- x)/(x^3)) =((1)/(3)+(1)/(2)+(1)/(6))/((1)/(2))=2

JEE Main 20257 AprilEvening Shift

Exam: JEE Main
Year: 2025
Date: 7 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Limits

JEE Main 2025 · 7 April · Evening Shift · Mathematics · Limits

If the function f(x)=( ( x)- ( x))/( x- x) is continuous at x=0 ,...

If the function

f(x)=\frac{\tan (\tan x)-\sin (\sin x)}{\tan x-\sin x}

is continuous at

\mathrm{x}=0

, then

f(0)

is equal to ________

Correct answer

Step-by-step solution

\lim _{x \rightarrow 0} \frac{\frac{\tan (\tan x)-\tan x}{\tan ^3 x} \frac{\tan ^3 x}{x^3}+\frac{\tan x-\sin x}{x^3}+\frac{\sin x-\sin (\sin x)}{\sin ^3 x} \frac{\sin ^3 x}{x^3}}{\frac{\tan x-\sin x}{x^3}}

=\frac{\frac{1}{3}+\frac{1}{2}+\frac{1}{6}}{\frac{1}{2}}=2

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