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

1. ali2x2

2. anonymous

You could approach this using limits, or you could 1) Evaluate f(x) for x just larger than 2, say 2.001 2) Evaluate f(x) for x just less than 2, say 1.999 3) Choose the value between these two.

3. anonymous

You might even be able to graph the function and determine the limit at x=2.

4. ali2x2

ospreytriple makes me look like dirt >:o

5. ali2x2

:P

6. ali2x2

nahhhh