CBSE Class 11-science Answered

Asked by Topperlearning User | 10 Nov, 2016, 01:57: AM

Expert Answer

$limit as x rightwards arrow a of open parentheses fraction numerator a sin x minus x sin a over denominator a x squared minus a squared x end fraction close parentheses equals limit as x rightwards arrow a of open parentheses fraction numerator a sin x minus x sin a plus x sin x minus x sin x over denominator a x left parenthesis x minus a right parenthesis end fraction close parentheses equals limit as x rightwards arrow a of open parentheses fraction numerator left parenthesis a minus x right parenthesis sin x plus x left parenthesis sin x minus sin a right parenthesis over denominator a x left parenthesis x minus a right parenthesis end fraction close parentheses equals limit as x rightwards arrow a of fraction numerator negative sin x over denominator a x end fraction plus limit as x rightwards arrow a of fraction numerator sin x minus sin a over denominator a left parenthesis x minus a right parenthesis end fraction equals negative sin over a squared plus limit as x rightwards arrow a of fraction numerator 2 cos open parentheses begin display style fraction numerator x plus a over denominator 2 end fraction end style close parentheses sin begin display style fraction numerator x minus a over denominator 2 end fraction end style over denominator 2 a open parentheses begin display style fraction numerator x minus a over denominator 2 end fraction end style close parentheses end fraction equals negative sin over a squared plus fraction numerator cos a over denominator a end fraction$