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solve and the answer of question is={discontinuous at x=1,4 & 5}
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Asked by adjacentcalliber10 | 07 May, 2019, 23:49: PM
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f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator 1 over denominator x minus 1 end fraction comma space space 0 less or equal than x less or equal than 2 end cell row cell table attributes columnalign left end attributes row cell fraction numerator 3 over denominator x plus 1 end fraction comma space 2 less than x less or equal than 4 end cell row cell fraction numerator x plus 1 over denominator x minus 5 end fraction comma space 4 less than x less or equal than 6 end cell end table end cell end table close C l e a r l y comma space t h e space f u n c t i o n space f space i s space n o t space d e f i n e d space a t space x equals 1 space a n d space x minus 5 space sin c e space f left parenthesis 1 right parenthesis equals fraction numerator 1 over denominator 1 minus 1 end fraction equals 1 over 0 space a n d space f left parenthesis 5 right parenthesis equals fraction numerator 5 plus 1 over denominator 5 minus 5 end fraction space i. e. space u n d e f i n e d S o space i t space i s space d i s c o n t i n u o u s space a t space x equals 1 space a n d space x equals 5 N o w comma space w e space n e e d space t o 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 x equals 2 space a n d space x equals 4 space b e c a u s e space f space c h a n g e s space a t space t h e s e space v a l u e s F o r space x equals 2 L H L equals limit as x rightwards arrow 2 to the power of minus of f left parenthesis x right parenthesis equals limit as x rightwards arrow 2 of space fraction numerator 1 over denominator x minus 1 end fraction equals 1 R H L equals limit as x rightwards arrow 2 to the power of plus of f left parenthesis x right parenthesis equals limit as x rightwards arrow 2 of space fraction numerator 3 over denominator x plus 1 end fraction equals 1 T h e r e f o r e comma space L H L equals R H L T h u s comma space f space i s space c o n t i n u o u s space a t space x equals 2. N o w comma space f o r space x equals 4 L H L equals limit as x rightwards arrow 4 to the power of minus of f left parenthesis x right parenthesis equals limit as x rightwards arrow 4 of space fraction numerator 3 over denominator x plus 1 end fraction equals 3 over 5 R H L equals limit as x rightwards arrow 4 to the power of plus of f left parenthesis x right parenthesis equals limit as x rightwards arrow 4 of space fraction numerator x plus 1 over denominator x minus 5 end fraction equals negative 5 T h e r e f o r e comma space L H L not equal to R H L T h u s comma space f space i s space n o t space c o n t i n u o u s space a t space x equals 4. H e n c e space t h e space p o i n t s space o f space d i s c o n t i n u i t i e s space a r e space 1 comma space 4 space a n d space 5.
Answered by Renu Varma | 08 May, 2019, 10:23: AM

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JEE main - Maths
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