Let f : R → R be a function such that f 2 = 4 and f ' 2 = 1 . Then, the value of lim x → 2 x 2 f 2 - 4 f x x - 2 is equal to:

Given, f 2 = 4 So, the given limit is in 0 0 form. So, lim x → 2 x 2 f 2 - 4 f x x - 2 Apply L 'Hospital Rule lim x → 2 2 x f 2 - 4 f ' x 1 = 4 4 - 4 1 = 12

Home
PYQ PracticeFree
JEE Rank Predictor
Answer Key

Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsAlgebraic and Rational LimitsEasy2 minPYQ_2021

MathematicsEasysingle choice

Let $f : R \to R$ be a function such that $f (2) = 4$ and $f^{'} (2) = 1 .$ Then, the value of $\lim_{x \to 2} \frac{x^{2} f (2) - 4 f (x)}{x - 2}$ is equal to:

Options:

Answer:

Solution:

Given, $f (2) = 4$

So, the given limit is in $\frac{0}{0}$ form.

So, $\lim_{x \to 2} \frac{x^{2} f (2) - 4 f (x)}{x - 2}$

Apply $L$ 'Hospital Rule

$\lim_{x \to 2} (\frac{2 x f (2) - 4 f^{'} (x)}{1})$

$= \frac{4 (4) - 4}{1} = 12$

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

⏱ 2mℹ️ Source: PYQ_2021

Doubts & Discussion

Loading discussions...