Question

lim x->
sqrt(x-4)-1/x-13

HELP PLEASE

Answer 1

\[\lim x->13 (\sqrt{x-4}-3)/x-13\]

Answer 2

do you know L-Hospital rule??

Answer 3

No...

Answer 4

if we get stuck in limit like this

we apply L-Hospital rule

which state....

take the derivative of numerator and denominator

and then apply the given limit

Answer 5

can you do it now??

Answer 6

I'm not sure what you mean...ugh

Answer 7

I come up with zero

Answer 8

yes this is the right answer

Answer 9

\[\lim_{x\to13}\frac{\sqrt{x-4}-3}{x-13}\cdot\frac{\sqrt{x-4}+3}{\sqrt{x-4}+3}\\
\lim_{x\to13}\frac{(x-4)-9}{(x-13)(\sqrt{x-4}+3)}\\
\lim_{x\to13}\frac{x-13}{(x-13)(\sqrt{x-4}+3)}\\
\lim_{x\to13}\frac{1}{\sqrt{x-4}+3}\]