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Asked by adjacentcalliber10 | 08 May, 2019, 23:47: PM
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f left parenthesis x right parenthesis equals open square brackets fraction numerator e to the power of x minus 1 over denominator x end fraction close square brackets space i f space 0 less than x less or equal than 1 S i n c e space space 0 less than x less or equal than 1 rightwards double arrow e to the power of 0 less than e to the power of x less or equal than e to the power of 1 rightwards double arrow 0 less than e to the power of x minus 1 less or equal than e minus 1 S i n c e space 0 less than x less or equal than 1 rightwards double arrow infinity greater than 1 greater than fraction numerator e to the power of x minus 1 over denominator x end fraction greater or equal than fraction numerator e minus 1 over denominator x end fraction greater than e minus 1 rightwards double arrow 1 greater than fraction numerator e to the power of x minus 1 over denominator x end fraction greater or equal than 1.718 rightwards double arrow open square brackets fraction numerator e to the power of x minus 1 over denominator x end fraction close square brackets equals 1 space i f space space 0 less than x less or equal than 1 rightwards double arrow limit as x rightwards arrow 0 of open square brackets fraction numerator e to the power of x minus 1 over denominator x end fraction close square brackets equals 1 S i n c e space f space i s space c o n t i n u o u s space f o r space a l l space x element of left square bracket negative 1 comma 2 right square bracket rightwards double arrow f space i s space c o n t i n u o u s space a t space x equals 0 rightwards double arrow limit as x rightwards arrow 0 to the power of minus of f left parenthesis x right parenthesis equals limit as x rightwards arrow 0 to the power of plus of f left parenthesis x right parenthesis rightwards double arrow limit as x rightwards arrow 0 of a x plus b equals limit as x rightwards arrow 0 of open square brackets fraction numerator e to the power of x minus 1 over denominator x end fraction close square brackets equals 1 rightwards double arrow b equals 1 S i m i l a r l y comma space f space i s space c o n t i n u o u s space a t space x equals 1 rightwards double arrow limit as x rightwards arrow 1 to the power of minus of f left parenthesis x right parenthesis equals limit as x rightwards arrow 1 to the power of plus of f left parenthesis x right parenthesis rightwards double arrow limit as x rightwards arrow 1 of space left parenthesis 1 right parenthesis equals limit as x rightwards arrow 1 of space b x plus a rightwards double arrow 1 equals b plus a rightwards double arrow a equals 0
Answered by Renu Varma | 09 May, 2019, 10:26: AM

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