Question

f(x) -f(2) /x-2 , limita x tinde la 2

Answer 1

x-2 tinde la 0 plus deci 1/(x-2) tinde la ∞
1) daca f(2)<0 atunci limita este ∞
2) daca f(2)>0 atunci limita este -∞
3) daca f(2)=0 atunci limita e 0

O seara buna!

Answer 2

$f(x)=lnx- \frac{1}{x}$

$\lim_{x \to \ 2 \frac{f(x)-f(2)}{x-2}=f`(2)$


f`(x)=(lnx)`-$( \frac{1}{x}) `$

$( \frac{1}{x}) `= \frac{1`*x-1*x`}{x^2} = \frac{-1}{x^2}$

$f`(x)= \frac{1}{x}+ \frac{1}{x^2}$

$f`(2)= \frac{1}{2}+ \frac{1}{2^2}= \frac{1}{2}+ \frac{1}{4}= \frac{2+1}{4}= \frac{3}{4}$