Question

lim of ( sqrt root (4x+1) - 3 over x-2 ) as x approaches 2

Answer 1

\[\lim_{x\to 2}\frac{\sqrt{4x+1}-3}{x-2}\] rationalize the numerator

Answer 2

\[\frac{\sqrt{4x+1}-3}{x-2}\times \frac{\sqrt{4x+1}+3}{\sqrt{4x+1}+3}\]
\[=\frac{4x+1-9}{(x-2)(\sqrt{4x+1}+3)}\]
\[=\frac{4(x-2)}{(x-2)(\sqrt{4x+1}+3)}\]
\[=\frac{4}{\sqrt{4x+1}+3}\]

Answer 3

now replace \(x\) by \(2\) to take your limit