Question

Fie functia f:R cu valori in R f(x)=x+1 supra x-1.calculati lim x extinde la-1 f(x)-f(-1) supra x+1

Answer 1

[tex] \lim_{x \to \ 1 } \frac{f(x)-f(-1)}{x+1} =f`(-1) [/tex]

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

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