This Sage tool will let you table the values of the expression\[\frac{b^h-1}{h}\] for values of \(h\) on either side of \(h=0\) for different values of the base \(b\).

From this numerical evidence you can estimate\[\lim_{h\rightarrow 0}\,\frac{b^h-1}{h}\]

Be sure to try \(b=e\approx 2.718281828\).