Let f: R arrow R be a function such that f(2)=4 and f'(2)=1. Then, the value of displaystyle lim x arrow 2 (x2 f(2)-4 f(x)/x-2) is equal to :

Question

Let f: R arrow R be a function such that f(2)=4 and f'(2)=1. Then, the value of displaystyle lim x arrow 2 (x2 f(2)-4 f(x)/x-2) is equal to : (A) 4 (B) 8 (C) 16 (D) 12

Tardigrade Admin · Accepted Answer

Apply L'Hopital Rule displaystyle lim x arrow 2((2 x f(2)-4 f'(x)/1)) =(4(4)-4/1)=12

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

4

8

16

12

Apply L'Hopital Rule
$x \to 2 lim (\frac{2 x f ( 2 ) - 4 f ^{'} ( x )}{1})$
$= \frac{4 ( 4 ) - 4}{1} = 12$

Q. Let f:R→R be a function such that f(2)=4 and f′(2)=1. Then, the value of x→2lim​x−2x2f(2)−4f(x)​ is equal to :

4

8

16

12

Apply L'Hopital Rule x→2lim​(12xf(2)−4f′(x)​) =14(4)−4​=12

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

Apply L'Hopital Rule
$x \to 2 lim (\frac{2 x f ( 2 ) - 4 f ^{'} ( x )}{1})$
$= \frac{4 ( 4 ) - 4}{1} = 12$