Question

Estimate the limit lim

Answer 1

Answer:

Step-by-step explanation:

In order for that x to not be a problem, we need to get rid of it somehow in the denominator. That requires that we multiply the whole function by the conjugate of the numerator:

$\frac{\sqrt{x+2}-\sqrt{2} }{x}*\frac{\sqrt{x+2}+\sqrt{2} }{\sqrt{x+2}+\sqrt{2} }$ which gives us, when we simplify:

$\frac{x+2-2}{x(\sqrt{x+2}+\sqrt{2}) }$ which simplifies even further to:

$\frac{x}{x(\sqrt{x+2}+\sqrt{2}) }$ and cancelling out the x on top with the x on the bottom gives us:

$\frac{1}{\sqrt{x+2}+\sqrt{2} }$  Now we have no problems at all subbing in a 0 for x:

$\frac{1}{\sqrt{0+2}+\sqrt{2} }=\frac{1}{\sqrt{2}+\sqrt{2} }=\frac{1}{2\sqrt{2} }=.3535$