Let $f:R \to R$ be a differentiable function satisfying $f'(3) + f'(2) = 0.$ then $\mathop {\lim }\limits_{x \to 0} {\left( {\frac{{1 + f(3 + x) - f(3)}}{{1 + f(2 - x) - f(2)}}} \right)^{\frac{1}{x}}}$ is equal to

JEE MATHEMATICS MCQ: LIMITS

1 Easy

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Analyzing +4 | -1

Let

f:R \to R

be a differentiable function satisfying

f'(3) + f'(2) = 0.

then

\lim\limits_{x \to 0} {\left( {\frac{{1 + f(3 + x) - f(3)}}{{1 + f(2 - x) - f(2)}}} \right)^{\frac{1}{x}}}

is equal to

View answer and explanation

Correct option: D

Option D (1) is correct because applying L'Hopital's rule and using the given condition

f'(3) + f'(2) = 0

simplifies the limit to 1.

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