Step-by-step Solution

Evaluate the limit of $\frac{\sqrt{10-x}-4}{x+6}$ as $x$ approaches $-6$

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Step-by-step explanation

Problem to solve:

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

Learn how to solve limits problems step by step online.

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

Unlock this full step-by-step solution!

Learn how to solve limits problems step by step online. Evaluate the limit of ((10-x)^0.5-4)/(x+6) as x approaches -6. Applying rationalisation. Multiplying fractions. Solve the product of difference of squares \left(\sqrt{10-x}-4\right)\left(\sqrt{10-x}+4\right). Evaluate the limit by replacing all occurrences of x by -6.

Final Answer

$-\infty $

Problem Analysis

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

Main topic:

Limits

Time to solve it:

~ 0.1 seconds