Find the largest value of k for which the function defined by

http://www2.wolframalpha.com/Calcula...=image/gif&s=7

is continuous on the interval [3, 3+k) .

...Through aproximation I found that in order to stay in one "step" the interval has to be [3, <sqrt(10)) but I can't seem to find a way to find k algebraically from the beginning.