Question

If f(2)=4 and f'(2)=1, then find lim x tends to 2 xf(2)-2f(x)/x-2

Answer 1

$\lim_{x\to\;2} \frac{xf(2)-2f(x)}{x-2}$

$=\frac{2f(2)-2f(2)}{2-2}=\frac{0}{0}\;\;form$

$\text{Apply L Hopitols rule}$

$=\lim_{x\to\;2} \frac{f(2)-2f\,'(x)}{1}$

$=f(2)-2f\,'(2)$

$=4-2(1)$

$=4-2$

$=2$

$\therefore\boxed{\bf\lim_{x\to\;2} \frac{xf(2)-2f(x)}{x-2}=2}$

Find more:

Lim. 8x³-1 / 16x4-1

x--->1/2

https://brainly.in/question/6423235

Answer 2

Plz refer to the attachment for your answer

Hope it works (◕ᴗ◕✿)(ʘᴗʘ✿)