Question

f(x) = ln x-(1/x). Aratati ca lim (x->2) (f(x) - f(2))/x-2= 3/4. ​

Answer 1

$\it f(x)=lnx-\dfrac{1}{x}\\ \\ \\ f'(x)=\dfrac{x+1}{x^2}\\ \\ \\ lim_{x\rightarrow2}\dfrac{f(x)-f(2)}{x-2}=f'(2)=\dfrac{2+1}{2^2}=\dfrac{3}{4}$

Answer 2

Răspuns:

scriere corecta

(f(x) - f(2))/(x-2)= 3/4. ​

Explicație pas cu pas:

prin def.,  limita ceruta este f'(2)

f'(x) =1/x+1/x²

deci

f'(2) =1/2+1/4=3/4