If f(3) = 4 and f'(3) = 1, then displaystyle limx → 3 (xf(3)-3 f(x)/x-3)

Question

If f(3) = 4 and f'(3) = 1, then displaystyle limx → 3 (xf(3)-3 f(x)/x-3) (A) -1 (B) 2 (C) 3 (D) 1

Tardigrade Admin · Accepted Answer

We have, displaystyle limx → 3 (xf(3)-3 f(x)/x-3) = displaystyle limx → 3 ((x-3)f(3)+3 f(3)-f(x) /x-3) = displaystyle limx → 3((x-3)f(3)/x-3)+ displaystyle limx → 3(-3 f(x)-f(3) /x-3) =f(3)+(-3) displaystyle limx → 3 (f(x)-x(3)/x-3) =f(3)-3f'(3) =4-3×1=1.

Q. If $f (3) = 4$ and $f^{'} (3) = 1$ , then $x \to 3 lim$ $\frac{x f ( 3 ) - 3 f ( x )}{x - 3}$

$- 1$

$2$

$3$

$1$

Q. If f(3)=4 and f′(3)=1, then x→3lim​ x−3xf(3)−3f(x)​

−1

2

3

1

We have, x→3lim​ x−3xf(3)−3f(x)​ =x→3lim​ x−3(x−3)f(3)+3{f(3)−f(x)}​ =x→3lim​x−3(x−3)f(3)​+x→3lim​x−3−3{f(x)−f(3)}​ =f(3)+(−3)x→3lim​ x−3f(x)−x(3)​ =f(3)−3f′(3) =4−3×1=1.

Q. If $f (3) = 4$ and $f^{'} (3) = 1$ , then $x \to 3 lim$ $\frac{x f ( 3 ) - 3 f ( x )}{x - 3}$

$- 1$

$2$

$3$

$1$