Question

limits!
limit of sqrt(x+3)-sqrt(3x+1)/x-1 as x approaches 1

Answer 1

\[\lim_{x \rightarrow1} \frac{ \sqrt{x+3}-\sqrt{3x+1} }{x-1 }\]

Answer 2

rationalize

Answer 3

\[
L=\lim_{x\to1}\frac{ \sqrt{x+3}-\sqrt{3x+1} }{x-1}\times\frac{\sqrt{x+3}+\sqrt{3x+1}}{\sqrt{x+3}+\sqrt{3x+1}}
\]

Answer 4

\[L=\lim_{x\to1}\frac{(x+3)-(3x+1)}{(x-1)(\sqrt{x+3}+\sqrt{3x+1})}\]

Answer 5

ok and then do you plug in 1 for x?

Answer 6

can you? ;)

Answer 7

uh no...that gives me 0 on the denominator

Answer 8

exactly.. what was the point of doing that extra multiplication? .. simplify that numerator a little bit more

Answer 9

\[x+3-3x-1=-2x+2=-2(x-1)\]

Answer 10

got it! -1/2 thank you:)

Answer 11

yep.