Question

Evaluate the limit.

lim x---> 0 sqrt(x+1) - sqrt(2x+1)/sqrt(3x+4) - sqrt(2x+4)


I got lim x--> 0 -sqrt(3x+4)-sqrt(2x+4)/sqrt(x+1)+sqrt(2x+1)

Is there anyway to simplify it down further?

Answer 1

\[\lim_{x\to0}\frac{\sqrt{x+1}-\sqrt{2x+1}}{\sqrt{3x+4}-\sqrt{2x+4}}\cdot\frac{\sqrt{x+1}+\sqrt{2x+1}}{\sqrt{x+1}+\sqrt{2x+1}}\cdot\frac{\sqrt{3x+4}+\sqrt{2x+4}}{\sqrt{3x+4}+\sqrt{2x+4}}\\
\lim_{x\to0}\frac{x+1-(2x+1)}{3x+4-(2x+4)}\cdot\frac{\sqrt{3x+4}+\sqrt{2x+4}}{\sqrt{x+1}+\sqrt{2x+1}}\\
\lim_{x\to0}-\frac{x}{x}\cdot\frac{\sqrt{3x+4}+\sqrt{2x+4}}{\sqrt{x+1}+\sqrt{2x+1}}\\
\vdots
\]

Answer 2

Now you can just plug in the 0.

Answer 3

Ok, thanks

Answer 4

yw