Question

${lim}_{x\to 0}\frac{e^{3+x}-sinx-e^3}{x}$

Answer 1

${lim}_{x\to 0}\frac{e^{3+x}-sinx-e^3}{x}$

$={lim}_{x\to 0}\frac{e^3(e^x-1)-sinx}{x}$

$={lim}_{x\to 0}\frac{e^x-1}{x}-{lim}_{x\to 0}\frac{sinx}{x}$

$=e^{3}loge-1$

$=e^3-1$