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Asked by adjacentcalliber10 | 06 May, 2019, 22:59: PM
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G i v e n space t h a t colon space f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator 1 minus sinπ x over denominator 1 plus cos 2 πx end fraction comma space space space space space space space space space space space space x less than 1 half end cell row cell table attributes columnalign left end attributes row cell p comma space space space space space space space space space space space space space space space space space space space space space space space space space space space x equals 1 half end cell row cell fraction numerator square root of 2 x minus 1 end root over denominator square root of 4 plus square root of 2 x minus 1 end root end root minus 2 end fraction comma space x greater than 1 half end cell end table end cell end table close f space i s space c o n t i n u o u s space a t space x equals 1 half rightwards double arrow L H L equals R H L equals f open parentheses 1 half close parentheses equals p S o comma space w e space h a v e p equals limit as x rightwards arrow 1 half to the power of minus of space f left parenthesis x right parenthesis equals limit as x rightwards arrow 1 half to the power of plus of space f left parenthesis x right parenthesis T h e r e f o r e comma space w e space h a v e p equals limit as x rightwards arrow 1 half of open parentheses fraction numerator 1 minus sinπ x over denominator 1 plus cos 2 πx end fraction close parentheses equals limit as x rightwards arrow 1 half of open parentheses fraction numerator 1 minus sinπ x over denominator 1 plus 1 minus 2 sin squared πx end fraction close parentheses equals limit as x rightwards arrow 1 half of open parentheses fraction numerator 1 minus sinπ x over denominator 2 left parenthesis 1 minus sin squared πx right parenthesis end fraction close parentheses equals limit as x rightwards arrow 1 half of open parentheses fraction numerator 1 minus sinπ x over denominator 2 left parenthesis 1 minus sinπ x right parenthesis open parentheses 1 plus sinπ x close parentheses end fraction close parentheses equals limit as x rightwards arrow 1 half of open parentheses fraction numerator 1 over denominator 2 open parentheses 1 plus sinπ x close parentheses end fraction close parentheses equals 1 fourth H e n c e comma space p equals 1 fourth.
Answered by Renu Varma | 07 May, 2019, 09:41: AM

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