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$\lim\limits_{x \rightarrow 0}\left(\sin \frac{x}{m}+\cos \frac{3 x}{m}\right)^{\frac{2 m}{x}}$ is |
1 $e^2$ $e^{lm}$ log 6m |
$e^2$ |
$y=\lim\limits_{x \rightarrow 0}\left(\sin \frac{x}{m}+\cos \frac{3 x}{m}\right)^{\frac{2 m}{x}}$ $\log y=\lim\limits_{x \rightarrow 0}\frac{2 m}{x}\log \left(\sin \frac{x}{m}+\cos \frac{3 x}{m}\right) =\frac{0}{0}$ by L'hopital's rule $\log y=\lim\limits_{x \rightarrow 0}\frac{\frac{1}{m}\frac{\cos x}{m}-\frac{3}{m}\frac{\sin x}{m}}{\left(\frac{\sin x}{m}+\frac{\cos x}{m}\right)×\frac{1}{2m}}=2$ $y=e^2$ |
