Question

Find the value of b for which the limit exists

Answer 1

Find the value of b, b>=0, for which \[\lim_{x \rightarrow 0}\left\{ \frac{ \sqrt{6x + b} -2}{ x } \right\}\] exists.

Answer 2

not as hard as it looks
the denominator is going to zero, so the only hope of a limit to exist is if the numerator goes to zero as well

Answer 3

as x goes to zero, so does 6x, so you have to make sure that \(\sqrt{b}-2=0\) i.e. \(\sqrt{b}=2\)