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  • Choose the correct answer out of 4 options given against each Question 〖lim〗┬(θ→0) ((1-cos⁡4θ)/(1-cos⁡6θ )) is

Choose the correct answer out of 4 options given against each Question

\mathop{\lim }_{ \theta \rightarrow 0} \left( \frac{1-\cos 4 \theta }{1-\cos 6 \theta } \right) is

A.\frac{4}{9}

B.\frac{1}{2}

C.-\frac{1}{2}

D.-1

Answers (1)

\\ \mathop{\lim }_{ \theta \rightarrow 0} \left( \frac{1-\cos 4 \theta }{1-\cos 6 \theta } \right) \\ \\ =\mathop{\lim }_{ \theta \rightarrow 0} \left( \frac{2\sin ^{2}2 \theta }{2\sin ^{2}3 \theta } \right) \\ \\ =\mathop{\lim }_{ \theta \rightarrow 0} \left( \frac{\sin 2 \theta }{\sin 3 \theta } \right) ^{2}=\mathop{\lim }_{ \theta \rightarrow 0} \left( \frac{\frac{\sin 2 \theta }{2 \theta } *2 \theta }{ \left( \frac{\sin 3 \theta }{3 \theta } \right) *3 \theta } \right) ^{2}=\frac{4}{9} \\ \\

Hence, the answer is option A

 

Posted by

infoexpert21

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