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Home / Doubts and Solutions/JEE/Mathematics

Lim.        Cotx - Cosx÷(π -2x)³
x--π÷2

Asked by sudheerkapoor67 17th November 2017, 8:34 PM
Answered by Expert
Answer:
begin mathsize 16px style limit as straight x rightwards arrow straight pi over 2 of open parentheses fraction numerator cotx minus cosx over denominator open parentheses straight pi minus 2 straight x close parentheses cubed end fraction close parentheses equals limit as straight h rightwards arrow 0 of open parentheses fraction numerator cot open parentheses begin display style straight pi over 2 end style plus straight h close parentheses minus cos open parentheses straight pi over 2 plus straight h close parentheses over denominator open parentheses negative 2 straight h close parentheses cubed end fraction close parentheses equals limit as straight h rightwards arrow 0 of open parentheses fraction numerator cot open parentheses begin display style straight pi over 2 plus straight h end style close parentheses minus cos open parentheses straight pi over 2 plus straight h close parentheses over denominator open parentheses straight h close parentheses cubed end fraction close parentheses fraction numerator 1 over denominator negative 8 end fraction equals limit as straight h rightwards arrow 0 of open parentheses fraction numerator negative tan space straight h minus sinh over denominator open parentheses straight h close parentheses cubed end fraction close parentheses fraction numerator 1 over denominator negative 8 end fraction equals limit as straight h rightwards arrow 0 of open parentheses fraction numerator begin display style fraction numerator sin space straight h over denominator cos space straight h end fraction end style plus sinh over denominator open parentheses straight h close parentheses cubed end fraction close parentheses 1 over 8 equals limit as straight h rightwards arrow 0 of open parentheses fraction numerator begin display style sin space straight h space open parentheses fraction numerator 1 over denominator cos space straight h end fraction space plus 1 close parentheses end style over denominator open parentheses straight h close parentheses cubed end fraction close parentheses 1 over 8 equals limit as straight h rightwards arrow 0 of open parentheses fraction numerator begin display style sin space straight h space open parentheses fraction numerator 1 plus cos space straight h over denominator cos space straight h end fraction close parentheses end style over denominator open parentheses straight h close parentheses cubed end fraction close parentheses 1 over 8 equals limit as straight h rightwards arrow 0 of open parentheses fraction numerator begin display style sin space straight h space open parentheses fraction numerator 2 sin squared begin display style straight h over 2 end style over denominator cos space straight h end fraction close parentheses end style over denominator open parentheses straight h close parentheses cubed end fraction close parentheses 1 over 8 .......... adjust space terms space use space limit as straight h rightwards arrow 0 of fraction numerator sin space straight h over denominator straight h end fraction equals 1 comma space get space ans space end style
Answered by Expert 5th December 2017, 4:20 PM
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