Step-by-step solution
Problem to solve:
$\lim_{x\to\:10}\left(\frac{\sqrt{x+6}-4}{x-10}\right)$
Solving method
Learn how to solve limits problems step by step online.
$\lim_{x\to10}\left(\frac{\sqrt{x+6}-4}{x-10}\frac{\sqrt{x+6}+4}{\sqrt{x+6}+4}\right)$
Learn how to solve limits problems step by step online. Find the limit (x)->(10)lim(((x+6)^0.5-4)/(x-10)). Applying rationalisation. Multiplying fractions \frac{\sqrt{x+6}-4}{x-10} \times \frac{\sqrt{x+6}+4}{\sqrt{x+6}+4}. Solve the product of difference of squares \left(\sqrt{x+6}-4\right)\left(\sqrt{x+6}+4\right). Simplify the fraction \frac{-10+x}{\left(x-10\right)\left(\sqrt{x+6}+4\right)} by -10+x.
Final Answer
$\frac{1}{8}$$\,\,\left(\approx 0.125\right)$