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December 23rd, 2018, 06:13 AM  #1 
Member Joined: Feb 2018 From: Iran Posts: 38 Thanks: 3  Limit problem How can I solve this question without using derivatives? Last edited by Elize; December 23rd, 2018 at 06:18 AM. 
December 23rd, 2018, 06:26 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,634 Thanks: 2620 Math Focus: Mainly analysis and algebra 
Multiply numerator and denominator by $\cos x +\sqrt{\cos 2x}$.

December 24th, 2018, 07:25 AM  #3 
Member Joined: Feb 2018 From: Iran Posts: 38 Thanks: 3  
December 24th, 2018, 08:37 AM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,634 Thanks: 2620 Math Focus: Mainly analysis and algebra 
\begin{align}(\cos x  \sqrt{\cos 2x})(\cos x + \sqrt{\cos 2x}) &= \cos^2 x  \cos 2x \\ &= \cos^2 x  (\cos^2 x  \sin^2 x) \\ &= \sin^2 x\end{align}


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