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Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsAlgebraic and Rational LimitsMedium2 minPYQ_2021

MathematicsMediumsingle choice

Let $f (x)$ be a differentiable function at $x = a$ with $f^{'} (a) = 2$ and $f (a) = 4$ . Then $\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}$ equals:

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Answer:

Solution:

$f^{'} (a) = 2, f (a) = 4$

$\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}$

$\Rightarrow \lim_{x \to a} \frac{f (a) - a f^{'} (x)}{1}$ (L'Hospitals rule)

$= f (a) - a f^{'} (a)$

$= 4 - 2 a$

Stream:JEESubject:MathematicsTopic:LimitsSubtopic:Algebraic and Rational Limits

⏱ 2mℹ️ Source: PYQ_2021

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