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Asked by sarveshvibrantacademy | 02 May, 2019, 00:11: AM
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g left parenthesis f left parenthesis x right parenthesis right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell g open parentheses fraction numerator x over denominator sin x end fraction close parentheses comma space x greater than 0 end cell row cell g left parenthesis 2 minus x right parenthesis comma space space x less or equal than 0 end cell end table close T h e r e a r e space t h r e e space d i f f e r e n t space c a s e s space f o r space g open parentheses fraction numerator x over denominator sin x end fraction close parentheses comma space x greater than 0 g open parentheses fraction numerator x over denominator sin x end fraction close parentheses equals fraction numerator x over denominator sin x end fraction plus 3 space i f space x greater than 0 space a n d space x less than 1 space i. e. space 0 less than x less than 1 g open parentheses fraction numerator x over denominator sin x end fraction close parentheses equals open parentheses fraction numerator x over denominator sin x end fraction close parentheses squared minus 2 fraction numerator x over denominator sin x end fraction minus 2 comma space w h e n space 1 less or equal than x less than 2 g open parentheses fraction numerator x over denominator sin x end fraction close parentheses equals fraction numerator x over denominator sin x end fraction minus 5 comma space w h e n space x greater or equal than 2 W h e n space x less or equal than 0 rightwards double arrow x less than 1 rightwards double arrow g left parenthesis f left parenthesis x right parenthesis right parenthesis equals g left parenthesis 2 minus x right parenthesis equals 2 minus x plus 3 space comma space x less or equal than 0 N o w comma space L H L equals limit as x rightwards arrow 0 to the power of minus of space g left parenthesis f left parenthesis x right parenthesis right parenthesis equals limit as x rightwards arrow 0 of space 2 minus x plus 3 equals 2 plus 3 equals 5 R H L equals limit as x rightwards arrow 0 to the power of plus of space g left parenthesis f left parenthesis x right parenthesis right parenthesis equals limit as x rightwards arrow 0 of fraction numerator x over denominator sin x end fraction plus 3 equals limit as x rightwards arrow 0 of fraction numerator 1 over denominator fraction numerator sin x over denominator x end fraction end fraction plus 3 equals 1 plus 3 equals 4 S i n c e comma space L H L not equal to R H L H e n c e comma space space limit as x rightwards arrow 0 of space g left parenthesis f left parenthesis x right parenthesis right parenthesis space d o e s space n o t space e x i s t.
Answered by Renu Varma | 02 May, 2019, 10:39: AM

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