Question

find the limit

Answer 1

\[\lim_{x \rightarrow 0}\frac{ \sqrt{x+5}-\sqrt{5} }{ x }\]

Answer 2

rationalize the numerator

Answer 3

so square everything on top?

Answer 4

no multiply by the conjugate

Answer 5

(a-b)(a+b)=a^2-b^2

Answer 6

multiply by the conjugate: \[\sqrt{x+5} + \sqrt{5}\] the numerator and denominator. then simplify....

Answer 7

ok so \[\frac{ \sqrt{x+5}-\sqrt{5} }{ x }*\frac{ \sqrt{x+5}+\sqrt{5} }{ \sqrt{x+5}+\sqrt{5} }\]
and you get
\[\frac{ x+5-5 }{ x(\sqrt{x+5}+\sqrt{5}) }\]

Answer 8

yes now simplify

Answer 9

so \[\frac{ 1 }{ \sqrt{x+5}+\sqrt{5} }\]

Answer 10

yes...

Answer 11

and the answer would be \[\frac{ 1 }{ 2\sqrt{5} }\]

Answer 12

rationalize the denom

Answer 13

\[\frac{ \sqrt{5} }{ 10 }\]

Answer 14

yes :)

Answer 15

thank you

Answer 16

no prob - that kind of problem is a classic for limits