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Question Number 30657 by NECx last updated on 23/Feb/18

lim_(x→∞)  e^(−(x^2 /2))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{e}^{−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}} \\ $$

Commented by Cheyboy last updated on 23/Feb/18

lim_(x→∞) e^(− (∞^2 /2))     lim_(x→∞)  e^(−∞)     lim_(x→∞ )  (1/e^∞ )   As x increases approching ⇒∞   (1/e^∞ ) approches 0    Hence lim_(x→∞)  (1/e^∞ ) =0

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}{e}^{−\:\frac{\infty^{\mathrm{2}} }{\mathrm{2}}} \\ $$$$ \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{e}^{−\infty} \\ $$$$ \\ $$$$\underset{{x}\rightarrow\infty\:} {\mathrm{lim}}\:\frac{\mathrm{1}}{{e}^{\infty} } \\ $$$$\:{As}\:{x}\:{increases}\:{approching}\:\Rightarrow\infty\: \\ $$$$\frac{\mathrm{1}}{{e}^{\infty} }\:{approches}\:\mathrm{0} \\ $$$$ \\ $$$${Hence}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{{e}^{\infty} }\:=\mathrm{0} \\ $$$$ \\ $$

Commented by NECx last updated on 25/Feb/18

thank you sir.

$${thank}\:{you}\:{sir}. \\ $$

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