Question

Find the limit as x approaches infinity

Answer 1

\[\lim_{x \rightarrow \infty}\frac{ \sqrt{x^{2}-4} }{ 4x-10 }\]

Answer 2

The numerator is factorable

Answer 3

And as a hint : \(\color{blue}{a^2 - b^2} = \color{red}{(a+b)(a-b)}\)

Answer 4

extract x from numerator
extract x from denominator
cancel x
then you have (number-0)/(number-0) <-- comes from taking the limit already

Answer 5

Yeah, I knew that it was factorable, but I don't really know how it helps.

Answer 6

Can you factor that out @selda31 : \(\sqrt{x^2 - 4}\) it is in the form of \(a^2-b^2\) , use the identity stated above to factorize it.

Answer 7

@mathslover Already did, but again, I don't know what to do after factoring it..

Answer 8

Try
\[\huge \frac{\sqrt{x^2(1-\frac{4}{x^2})}}{x(4-\frac{10}{x})} \\ \\ \huge \frac{x \sqrt{(1-\frac{4}{x^2})}}{x(4-\frac{10}{x})} \\ \\ \frac{ \sqrt{(1-\frac{4}{x^2})}}{(4-\frac{10}{x})}\]

Answer 9

^^

Answer 10

As
\[x \rightarrow \infty , \\ \\ =\frac{1}{4}\]

Answer 11

Oh okay, now I get it. Thanks a lot people