Question

lim(3x-15/(sqrt(x)-sqrt(5)))
x->5

Answer 1

Are you allowed L'Hospital? It makes it easy ...

Answer 2

Its homework, so yeah.

Answer 3

=lim 3(x-5).(sqrt(x)+sqrt(5))/(x - 5) ... just rationalizing the fraction
x->5
=lim 3.(sqrt(x)+sqrt(5))
x->5
= 3 (2sqrt(5)
=6sqrt(5)

Answer 4

I think this is sufficient right?????

Answer 5

hmm okay lets avoid l'hospital lets do algebra
\[\lim_{x\to5} \frac{3(x - 5)}{\sqrt x -\sqrt x }\implies \frac{3(\cancel{(\sqrt x - \sqrt 5)}(\sqrt 5 + \sqrt x)}{\cancel{\sqrt x -\sqrt 5}}\]

Answer 6

Yep. That's the way.

Answer 7

\[3( \sqrt 5 + \sqrt 5 ) \implies 3*2\sqrt 5\]

Answer 8

If you have any doubts then do ask them :]

Answer 9

It's right. Thanks! :)