If f:R→ R be a differentiable function such that f(4)=6 and f'(4)=2, then undersetx→ 4 mathop lim (x f(4)-4f(x)/x-4) is equal to

Question

If f:R→ R be a differentiable function such that f(4)=6 and f'(4)=2, then undersetx→ 4 mathop lim (x f(4)-4f(x)/x-4) is equal to (A)  2  (B)  -2  (C)  0  (D)  1

Tardigrade Admin · Accepted Answer

undersetx→ 4 mathop lim (x f(4)-4f(x)/x-4) = undersetx→ 4 mathop lim (f(4)-4f'(x)/1) =f(4)-4f'(4) =(6-4(2)/1)=6-8 =-2

Q. If $f : R \to R$ be a differentiable function such that $f (4) = 6$ and $f^{'} (4) = 2,$ then $x \to 4 lim \frac{x f ( 4 ) - 4 f ( x )}{x - 4}$ is equal to

$2$

$- 2$

$0$

$1$

$x \to 4 lim \frac{x f ( 4 ) - 4 f ( x )}{x - 4}$
$= x \to 4 lim \frac{f ( 4 ) - 4 f ^{'} ( x )}{1}$
$= f (4) - 4 f^{'} (4)$ $= \frac{6 - 4 ( 2 )}{1} = 6 - 8$
$= - 2$

Q. If f:R→R be a differentiable function such that f(4)=6 and f′(4)=2, then x→4lim​x−4xf(4)−4f(x)​ is equal to

2

−2

0

1

x→4lim​x−4xf(4)−4f(x)​ =x→4lim​1f(4)−4f′(x)​ =f(4)−4f′(4) =16−4(2)​=6−8 =−2

Q. If $f : R \to R$ be a differentiable function such that $f (4) = 6$ and $f^{'} (4) = 2,$ then $x \to 4 lim \frac{x f ( 4 ) - 4 f ( x )}{x - 4}$ is equal to

$2$

$- 2$

$0$

$1$

$x \to 4 lim \frac{x f ( 4 ) - 4 f ( x )}{x - 4}$
$= x \to 4 lim \frac{f ( 4 ) - 4 f ^{'} ( x )}{1}$
$= f (4) - 4 f^{'} (4)$ $= \frac{6 - 4 ( 2 )}{1} = 6 - 8$
$= - 2$