Question

Se considera functia f:(2,+∞)⇒R
f(x)=x-1/x-2
a) Aratati ca$\lim_{x \to 3$ f(x)=2
b) Aratati ca f '(x)=-1/(x-2) la puterea2 x∈(2,+∞)

Answer 1

Lim (x- > 3) x-1/x-2=3-1/3-2=2, f'x=[(x-1)'(x-2)-(x-2)'(x-1)]/(x-2)^2=(x-2-x+1)/(x-2)^2=-1/(x-2)^2