lopezjas
lopezjas
15-08-2017
Mathematics
contestada
lim theta-->0 of sin6theta cubed over 7theta
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LammettHash
LammettHash
15-08-2017
[tex]\displaystyle\lim_{\theta\to0}\frac{\sin^36\theta}{7\theta}[/tex]
[tex]=\displaystyle\lim_{\theta\to0}\frac{(6\theta)^3\sin^36\theta}{7\theta(6\theta)^3}[/tex]
[tex]=\displaystyle\lim_{\theta\to0}\frac{(6\theta)^3}{7\theta}\times\lim_{\theta\to0}\frac{\sin^36\theta}{(6\theta)^3}[/tex]
[tex]=\displaystyle\frac{6^3}7\lim_{\theta\to0}\theta^2\times\left(\lim_{\theta\to0}\frac{\sin6\theta}{6\theta}\right)^3[/tex]
[tex]=\displaystyle\frac{6^3}7\times0\times1^3[/tex]
[tex]=0[/tex]
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