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Asked by g_archanasharma | 02 Mar, 2019, 19:39: PM
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begin mathsize 12px style limit as x rightwards arrow straight pi over 2 of fraction numerator sin open parentheses x space cos x close parentheses over denominator cos open parentheses x space sin x close parentheses end fraction end style
 
if we apply the limit to both numerator and denominator we get 0/0
 
Hence we apply L'Hospital rule
 
begin mathsize 12px style limit as x rightwards arrow straight pi over 2 of fraction numerator sin open parentheses x space cos x close parentheses over denominator cos open parentheses x space sin x close parentheses end fraction space equals space limit as x rightwards arrow straight pi over 2 of space fraction numerator cos left parenthesis x space cos space x right parenthesis space open square brackets cos x space minus x space sin x close square brackets over denominator negative sin open parentheses x space sin x close parentheses open square brackets sin x space plus x space cos x close square brackets end fraction space equals space fraction numerator cos open parentheses straight pi over 2 space cos straight pi over 2 close parentheses open square brackets cos straight pi over 2 space minus space straight pi over 2 sin straight pi over 2 close square brackets over denominator sin open parentheses straight pi over 2 sin straight pi over 2 close parentheses open square brackets sin straight pi over 2 space plus space straight pi over 2 space cos straight pi over 2 close square brackets end fraction space equals fraction numerator cos left parenthesis 0 right parenthesis open square brackets 0 space minus straight pi over 2 close square brackets over denominator negative sin straight pi over 2 left square bracket 1 plus 0 right square bracket end fraction space equals straight pi over 2 end style
Answered by Thiyagarajan K | 02 Mar, 2019, 22:44: PM

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