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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 16th November 2016, 2:20 AM
Answered by 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.

Answered by Expert 16th November 2016, 4:20 AM
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