I want to find $$ \lim_{x\to 2} \frac{x-\sqrt{x+2}}{\sqrt{4x+1} -3} $$ but without using derivatives, and l'Hopital.
I tried to rationalize and it didn't work. Could anyone help please?
2026-03-26 17:53:27.1774547607
How to find $ \lim_{x\to 2} \frac{x-\sqrt{x+2}}{\sqrt{4x+1} -3} $ without derivatives and l'Hopital?
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Hint: $$\lim_{x\to2}\dfrac{x-\sqrt{x+2}}{\sqrt{4x+1}-3}\times\dfrac{\sqrt{4x+1}+3}{\sqrt{4x+1}+3}\times\dfrac{x+\sqrt{x+2}}{x+\sqrt{x+2}} = \lim_{x\to2}\dfrac{(x+1)(x-2)}{4(x-2)}\times\dfrac{\sqrt{4x+1}+3}{x+\sqrt{x+2}}$$