Question

if k>0, lim as x approaches k (√x-√k)/(k-x), what is the limit?

Answer 1

x is the variable , k is a constant.

So if we were to sub x=k into the expression we would get 0/0 (indeterminate form). So use L Hopital's rule.

Differentiate top and bottom with respect to the VARIABLE (i.e. k is treated as a constant).


= l\[\lim_{x \rightarrow k} \frac{ \frac{1}{2 \sqrt{x}} - 0 }{0-1} = -\frac{1}{2\sqrt{k}}\]