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  • Evaluating  <img alt="\mathrm{\lim _{x \rightarrow 0} \frac{\sqrt[3]{\cos 4 x}-\sqrt[3]{\cos 5 x}}{1-\cos 3 x}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Clim%20

Evaluating  \mathrm{\lim _{x \rightarrow 0} \frac{\sqrt[3]{\cos 4 x}-\sqrt[3]{\cos 5 x}}{1-\cos 3 x}}

Option: 1

0


Option: 2

\frac{1}{3}


Option: 3

\frac{2}{5}


Option: 4

1


Answers (1)

best_answer

\mathrm{\frac{\sqrt[3]{\cos 4 x}-\sqrt[3]{\cos 5 x}}{1-\cos 3 x}=\frac{(\sqrt[3]{\cos 4 x}-\sqrt[3]{\cos 5 x}) *\left(\sqrt[3]{\cos ^2 4 x}+\sqrt[3]{\cos 4 x} * \sqrt[3]{\cos 4 x}+\sqrt[3]{\cos ^2 5 x}\right)}{(1-\cos 3 x) *\left(\sqrt[3]{\cos ^2 4 x}+\sqrt[3]{\cos 4 x} * \sqrt[3]{\cos 4 x}+\sqrt[3]{\cos ^2 5 x}\right)}}

                                           \mathrm{=\frac{\cos 4 x-\cos 5 x}{3(1-\cos 3 x)}}

 \mathrm{\lim _{x \rightarrow 0} \frac{1}{3} \frac{\cos (4 x)-\cos (5 x)}{1-\cos (3 x)}=\lim _{x \rightarrow 0} \frac{1}{3} \frac{1-\cos (3 x)}{1-\cos (3 x)}=\frac{1}{3}}

Posted by

Divya Prakash Singh

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