## zmudz one year ago For what value $$k$$ is the following function continuous at $$x=2$$? $$f(x) = \begin{cases} \frac{\sqrt{2x+5}-\sqrt{x+7}}{x-2} & x \neq 2 \\ k & x = 2 \end{cases}$$

for $$f(x)$$ to be continuous at $$x=2$$, we must hav $$\lim\limits_{x\to 2}f(x) = f(2)$$ that is : $\lim\limits_{x\to 2}\frac{\sqrt{2x+5}-\sqrt{x+7}}{x-2} = k$ do that conjugate thingy and try evaluating the limit