Question

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

Answer 1

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.

Answer 2

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

Answer 3

ospreytriple makes me look like dirt >:o

Answer 4

:P

Answer 5

nahhhh