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Limits by rationalizing Calculator

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1

Solved example of rationalisation

$\lim_{x\to-6}\left(\frac{\sqrt{10-x}-4}{x+6}\right)$
2

Aplicando racionalización

$\lim_{x\to-6}\left(\frac{\sqrt{10-x}-4}{x+6}\cdot\frac{\sqrt{10-x}+4}{\sqrt{10-x}+4}\right)$
3

Multiplicando fracciones

$\lim_{x\to-6}\left(\frac{\left(\sqrt{10-x}-4\right)\left(\sqrt{10-x}+4\right)}{\left(x+6\right)\left(\sqrt{10-x}+4\right)}\right)$
4

Resolver el producto $\left(\sqrt{10-x}-4\right)\left(\sqrt{10-x}+4\right)$

$\lim_{x\to-6}\left(\frac{\left(\sqrt{10-x}\right)^2-1\left(4^2\right)}{\left(x+6\right)\left(\sqrt{10-x}+4\right)}\right)$
5

Calcular la potencia $4^2$

$\lim_{x\to-6}\left(\frac{\left(\sqrt{10-x}\right)^2-1\cdot 16}{\left(x+6\right)\left(\sqrt{10-x}+4\right)}\right)$
6

Aplicamos la regla: $-x$, donde $x=16$

$\lim_{x\to-6}\left(\frac{\left(\sqrt{10-x}\right)^2-16}{\left(x+6\right)\left(\sqrt{10-x}+4\right)}\right)$
7

Aplicando la regla de potencia de una potencia

$\lim_{x\to-6}\left(\frac{10-x-16}{\left(x+6\right)\left(\sqrt{10-x}+4\right)}\right)$
8

Restar los valores $10$ y $-16$

$\lim_{x\to-6}\left(\frac{-6-x}{\left(x+6\right)\left(\sqrt{10-x}+4\right)}\right)$
9

Evaluando el límite cuando $x$ tiende a $-6$

$\frac{-6-1-6}{\left(-6+6\right)\left(\sqrt{10-1-6}+4\right)}$
10

Simplificando

$\frac{0}{0}$
11

$\frac{0}{0}$ representa una forma indeterminada

indeterminado

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