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A-lim-x-0-sinx-x-3-




Question Number 205448 by mathlove last updated on 21/Mar/24
A=lim_(x→0)  ((sinx)/x^3 )=?
$${A}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{sinx}}{{x}^{\mathrm{3}} }=? \\ $$
Answered by namphamduc last updated on 21/Mar/24
A=lim_(x→0)  ((sin(x))/x^3 )=lim_(x→0) ((sin(x))/x).x^4 =1.0=0
$${A}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\left({x}\right)}{{x}^{\mathrm{3}} }=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\left({x}\right)}{{x}}.{x}^{\mathrm{4}} =\mathrm{1}.\mathrm{0}=\mathrm{0} \\ $$
Commented by mathlove last updated on 21/Mar/24
lim_(x→0)  ((sin x)/x^3 )=lim_(x→0) ((sinx)/x)∙(1/x^2 )=1∙∞=∞
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}}{{x}^{\mathrm{3}} }=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{sinx}}{{x}}\centerdot\frac{\mathrm{1}}{{x}^{\mathrm{2}} }=\mathrm{1}\centerdot\infty=\infty \\ $$
Commented by A5T last updated on 21/Mar/24
((sin(x))/x^3 )≠((sin(x))/x).x^4 =sin(x).x^3
$$\frac{{sin}\left({x}\right)}{{x}^{\mathrm{3}} }\neq\frac{{sin}\left({x}\right)}{{x}}.{x}^{\mathrm{4}} ={sin}\left({x}\right).{x}^{\mathrm{3}} \\ $$

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