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solve the question and the answer is=(p is not possible)
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Asked by adjacentcalliber10 | 07 May, 2019, 23:51: PM
answered-by-expert Expert Answer
f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator 1 minus sin space πx over denominator 1 plus cos space 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 x equals 1 half space space space space space space space space space space space space 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 end cell end table comma space space x greater than 1 half end cell end table close L e t apostrophe s space c h e c k space t h e space c o n t i n u i t y space o f space f space a t space 1 half L H L equals limit as x rightwards arrow 1 half to the power of minus of f left parenthesis x right parenthesis equals limit as x rightwards arrow 1 half of fraction numerator 1 minus sin space πx over denominator 1 plus cos space 2 πx end fraction equals limit as x rightwards arrow 1 half of fraction numerator 1 minus sin space πx over denominator 2 left parenthesis 1 minus sin squared πx right parenthesis end fraction limit as x rightwards arrow 1 half of fraction numerator 1 over denominator 2 left parenthesis 1 plus sin space πx right parenthesis end fraction equals 1 fourth R H L equals limit as x rightwards arrow 1 half to the power of plus of f left parenthesis x right parenthesis equals limit as x rightwards arrow 1 half of 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 L e t space square root of 2 x minus 1 end root equals t comma space w h e n space x rightwards arrow 1 half comma space t rightwards arrow 0 R H L equals limit as t rightwards arrow 0 of fraction numerator t over denominator square root of 4 plus t end root minus 2 end fraction equals limit as t rightwards arrow 0 of fraction numerator t open parentheses square root of 4 plus t end root plus 2 close parentheses over denominator 4 plus t minus 4 end fraction equals limit as t rightwards arrow 0 of fraction numerator t open parentheses square root of 4 plus t end root plus 2 close parentheses over denominator t end fraction equals limit as t rightwards arrow 0 of space open parentheses square root of 4 plus t end root plus 2 close parentheses equals 4 S o comma space L H L not equal to R H L T h u s comma space t h e space f u n c t i o n space f space i s space n o t space c o n t i n u o u s space a t space 1 half T h e r e f o r e comma space f space i s space n o t space d e f i n e d space a t space 1 half H e n c e comma space p space d o e s space n o t space e x i s t space i. e. space i t space i s space n o t space p o s s i b e
Answered by Renu Varma | 08 May, 2019, 10:11: AM

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