CBSE Class 11-science Answered

$E v a l u a t e space limit as x rightwards arrow 0 of fraction numerator sin open vertical bar x close vertical bar over denominator x end fraction$ Please provide solution to this question

Asked by Topperlearning User | 16 Nov, 2016, 02:20: AM

Expert Answer

$space fraction numerator sin open vertical bar x close vertical bar over denominator x end fraction equals open curly brackets fraction numerator sin x over denominator x end fraction space f o r space x greater than 0 close curly brackets space space space space space space space space space space space space space space space space space space open curly brackets negative fraction numerator sin x over denominator x end fraction space f o r space x less than 0 close curly brackets L e f t space H a n d space l i m i t space equals limit as x rightwards arrow 0 to the power of minus of fraction numerator sin open vertical bar x close vertical bar over denominator x end fraction equals limit as h rightwards arrow 0 of minus fraction numerator sin h over denominator h end fraction equals negative 1 R i g h t space h a n d space l i m i t equals limit as x rightwards arrow 0 to the power of plus of fraction numerator sin open vertical bar x close vertical bar over denominator x end fraction equals limit as h rightwards arrow 0 of fraction numerator sin h over denominator h end fraction equals 1 L H L not equal to R H L space s o space t h e space l i m i t space d o e s n apostrophe t space e x i s t.$