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lim-x-0-e-x-2-2-cos-x-x-3-tan-x-




Question Number 130541 by EDWIN88 last updated on 26/Jan/21
 lim_(x→0)  ((e^(−x^2 /2) −cos x)/(x^3  tan x)) =?
$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{e}^{−{x}^{\mathrm{2}} /\mathrm{2}} −\mathrm{cos}\:{x}}{{x}^{\mathrm{3}} \:\mathrm{tan}\:{x}}\:=? \\ $$
Answered by Dwaipayan Shikari last updated on 26/Jan/21
lim_(x→0) ((1−(x^2 /2)+(x^4 /8)−1+(x^2 /2)−(x^4 /(24)))/x^4 )=(1/(12))
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+\frac{{x}^{\mathrm{4}} }{\mathrm{8}}−\mathrm{1}+\frac{{x}^{\mathrm{2}} }{\mathrm{2}}−\frac{{x}^{\mathrm{4}} }{\mathrm{24}}}{{x}^{\mathrm{4}} }=\frac{\mathrm{1}}{\mathrm{12}} \\ $$
Commented by EDWIN88 last updated on 26/Jan/21
✓
$$\checkmark \\ $$
Answered by EDWIN88 last updated on 26/Jan/21

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