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Question Number 79101 by mathmax by abdo last updated on 22/Jan/20
$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\frac{{sin}\left({e}^{−{x}^{\mathrm{2}} } \right)+{sinx}−{sin}\left(\mathrm{1}\right)}{{x}^{\mathrm{3}} } \\ $$
Commented by jagoll last updated on 23/Jan/20
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{−\mathrm{2xe}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{cos}\:\left(\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \right)+\mathrm{cos}\:\mathrm{x}}{\mathrm{3x}^{\mathrm{2}} }=\infty \\ $$$$ \\ $$