Question

Evaluate:

lim (sqrt x+2) -3 / x-7
x->7

Answer 1

use l'hopital and find the limits.....the answer will be,
1/6

Answer 2

\[\frac{\sqrt{x+2}-3}{x-7}\]
\[=\frac{\sqrt{x+2}-3}{x-7}\times \frac{\sqrt{x+2}+3}{\sqrt{x+2}+3}\]

Answer 3

\[=\frac{x+2-9}{(x-7)(\sqrt{x+2}+3}\]
\[=\frac{x-7}{(x-7)(\sqrt{x+2}+3}\]
\[=\frac{1}{\sqrt{x+2}+3}\]

Answer 4

replace x by 7, get
\[\frac{1}{\sqrt{7+2}+3}=\frac{1}{3+3}=\frac{1}{6}\]

Answer 5

thank you, now i know what i did wrong

Answer 6

it is true that l'hopital will give this as well, but usually these problems come before l'hopital and before derivatives

Answer 7

yw