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Asked by g_archanasharma | 15 May, 2019, 17:54: PM
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f left parenthesis x right parenthesis equals x cubed space sgn space x rightwards double arrow f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell x cubed comma space space space space space space x greater than 0 end cell row cell table attributes columnalign left end attributes row cell negative x cubed comma space space x less than 0 end cell row cell 0 comma space space space space space space x equals 0 end cell end table end cell end table close N o w comma space L H L equals limit as x rightwards arrow 0 to the power of minus of space f left parenthesis x right parenthesis equals limit as x rightwards arrow 0 of space left parenthesis negative x cubed right parenthesis equals 0 equals f left parenthesis 0 right parenthesis R H L equals limit as x rightwards arrow 0 to the power of plus of space f left parenthesis x right parenthesis equals limit as x rightwards arrow 0 of space x cubed equals 0 equals f left parenthesis 0 right parenthesis T h e r e f o r e comma space f space i s space c o n t i n u o u s. f apostrophe left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 3 x squared comma space space space space space space x greater than 0 end cell row cell table attributes columnalign left end attributes row cell negative 3 x squared comma space space space x less than 0 end cell row cell 0 comma space space space space space space space space space x equals 0 end cell end table end cell end table close f apostrophe left parenthesis 0 to the power of minus right parenthesis equals 0 equals f apostrophe left parenthesis 0 to the power of plus right parenthesis H e n c e comma space f space i s space d i f f e r e n t i a b l e space a t space x equals 0.
Answered by Renu Varma | 15 May, 2019, 18:48: PM

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