Question

${lim}_{x\to 5}\frac{e^x-e^5}{x-5}$

Answer 1

${lim}_{x\to 5}\frac{e^x-e^5}{x-5}$

Put $x=5+h$

$\Rightarrow h=x-5$

as $x\to 5,h\to 0$

$={lim}_{h\to 0}\frac{e^{5+h}-e^5}{h}$

$=e^5{lim}_{h\to 0}\frac{e^h-1}{h}$

$=e^5\times 1$

$=e^5$