Question

seja f(x) = x^2. então lim x-> 2 f(x) - f(2)/x - 2​

Answer 1

Temos que

$f(x) = {x}^{2} = > f(2) = {2}^{2} = 4$

Logo,

$\displaystyle\lim_{x \rightarrow2} \frac{f(x) - f(2)}{x - 2} = \displaystyle\lim_{x \rightarrow2} \frac{ {x}^{2} - 4}{x - 2} = \displaystyle\lim_{x \rightarrow2} \frac{(x + 2)(x - 2)}{x - 2} = \displaystyle\lim_{x \rightarrow2} x + 2 = 2 + 2 = 4$