bemath-lim-x-pi-1-2x-2pi-pi-x-cos-2t-dt-1-cos-3t-

Question Number 106869 by bemath last updated on 07/Aug/20

@ bemath @

\lim_{x \to π} [(\frac{1}{2 x - 2 π}) \underset{π}{\int^{x}} \frac{\cos 2 t dt}{1 - \cos 3 t}] = ?

Answered by bobhans last updated on 07/Aug/20

\overset{\land bobhans \land}{}

\lim_{x \to π} [\frac{\underset{π}{\int^{x}} \frac{\cos 2 t dt}{1 - \cos 3 t}}{2 x - 2 π}] = \lim_{x \to π} \frac{\frac{d}{dx} \int^{x} \frac{\cos 2 t dt}{1 - \cos 3 t}}{\frac{d}{dx} [2 x - 2 π]}

= \lim_{x \to π} \frac{(\frac{\cos 2 x}{1 - \cos 3 x})}{2} = \frac{\frac{1}{1 + 1}}{2} = \frac{1}{4}

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