Question

Seja f a função definida por f (x) = {x2 - 9 se x =/ -3}
{4 se x=-3}
Encontre:

Answer 1

$\small\boxed{\begin{array}{l}\rm f(x)=\begin{cases}\rm x^2-9,~se~~x\ne-3\\\rm ~~4~~~se~~x=-3\end{cases}\\\\\displaystyle\rm\lim_{ x\to -3^{+}}f(x)=\lim_{x \to -3}x^2-9=(-3)^2-9\\\\\displaystyle\rm\lim_{x \to -3}x^2-9=9-9=0.\\\\\displaystyle\rm\lim_{x \to -3^{-}}f(x)=\lim_{x \to -3} x^2-9=(-3)^2-9\\\\\displaystyle\rm\lim_{x \to -3}x^2-9=0\\\displaystyle\rm\lim_{x \to -3^{+}}f(x)=\lim_{x \to -3^{-}}f(x)\implies \lim_{x \to -3}f(x)=0\\\rm f(-3)=4\\\rm \end{array}}$

$\large\boxed{\begin{array}{l}\displaystyle\rm\lim_{x \to -3}f(x)\ne f(-3)\end{array}}$

$\large\boxed{\begin{array}{l}\sf b)~\rm o\,gr\acute afico\,est\acute a\,anexo.\end{array}}$