Question

Calcule o seguinte limite:

Answer 1

$\large\boxed{\begin{array}{l}\displaystyle\sf\lim_{x \to 3}\dfrac{5x^2-8x-13}{x^2-5}\\\\\sf note\,que\,substituindo\,x\,por\,3\\\sf n\tilde ao\,teremos\,indeterminac_{\!\!,}\tilde ao.\\\displaystyle\sf\lim_{x \to 3}\dfrac{5x^2-8x-13}{x^2-5}=\dfrac{5\cdot3^2-8\cdot3-13}{3^2-5}\\\\\displaystyle\sf\lim_{x \to 3}\dfrac{5x^2-8x-13}{x^2-5}=\dfrac{5\cdot9-24-13}{9-5}\\\\\displaystyle\sf\lim_{x \to 3}\dfrac{5x^2-8x-13}{x^2-5}=\dfrac{45-24-13}{4}=\dfrac{8}{4}=2\end{array}}$

Answer 2

$\Large\displaystyle\text{ \begin{gathered} \sf{ \lim_{x\to3}\frac{5x^2-8x-13}{x^2-5}=\frac{5\cdot3^2-8\cdot3-13}{3^2-5}} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ \lim_{x\to3}\frac{5x^2-8x-13}{x^2-5}=\frac{5\cdot9-8\cdot3-13}{9-5}} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{\lim_{x\to3}\frac{5x^2-8x-13}{x^2-5}=\frac{45-24-13}{4} } \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{\lim_{x\to3}\frac{5x^2-8x-13}{x^2-5}=\frac{ 45-37}{4}} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ \lim_{x\to3}\frac{5x^2-8x-13}{x^2-5}=\frac{8}{4}} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \therefore\red{\underline{\boxed{\boxed{\sf{\lim_{x\to3}\frac{5x^2-8x-13}{x^2-5}=2 } }}}}~~(\checkmark)\end{gathered} }$