Question Number 30553 by abdo imad last updated on 23/Feb/18
$${find}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \left(\mathrm{1}+{sinx}\right)^{{x}} \:−\left(\mathrm{1}+{x}\right)^{{sinx}} . \\ $$
Commented by Cheyboy last updated on 23/Feb/18
$${by}\:{direct}\:{subtitution} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{1}+\mathrm{0}\right)^{\mathrm{0}} −\left(\mathrm{1}+\mathrm{0}\right)^{\mathrm{0}} =\mathrm{0} \\ $$
Commented by abdo imad last updated on 23/Feb/18
$${forgive}\:{the}\:{Q}\:{is}\:{find}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{\left(\mathrm{1}+{sinx}\right)^{{x}} \:−\left(\mathrm{1}+{x}\right)^{{sinx}} }{{x}}\:. \\ $$
Commented by rahul 19 last updated on 23/Feb/18
$$\mathrm{simply}\:\mathrm{use}\:\mathrm{hospital}\:\mathrm{rule}\:. \\ $$