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Question Number 92079 by mathmax by abdo last updated on 04/May/20
$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{e}^{{sin}^{\mathrm{2}} {x}} −{e}^{{x}^{\mathrm{3}} −\mathrm{2}{x}} }{{x}^{\mathrm{2}} } \\ $$
Commented by john santu last updated on 05/May/20
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{2}{x}\:{e}^{\mathrm{sin}\:^{\mathrm{2}} {x}} −\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}\right){e}^{{x}^{\mathrm{3}} −\mathrm{2}{x}} }{\mathrm{2}{x}} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{e}^{\mathrm{sin}\:^{\mathrm{2}} {x}} \:\left(\frac{\mathrm{sin}\:\mathrm{2}{x}}{\mathrm{2}{x}}\right)\:−\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{e}^{{x}^{\mathrm{3}} −\mathrm{2}{x}} \left(\frac{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}}{\mathrm{2}{x}}\right) \\ $$$${D}\mathrm{NE}\: \\ $$