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Maths-

General

Easy

Question

If $f left parenthesis x right parenthesis equals left parenthesis 1 plus left square bracket x right square bracket right parenthesis to the power of fraction numerator 1 over denominator x minus left curly bracket x right curly bracket end fraction end exponent$ where $left square bracket x right square bracket$ and $open curly brackets x close curly brackets$ denote the integral part and fractional part of $x$ respectively and $a equals Lim subscript x not stretchy rightwards arrow 0 to the power of minus end subscript f left parenthesis x right parenthesis comma b equals Lim subscript x not stretchy rightwards arrow 0 to the power of plus end subscript f left parenthesis x right parenthesis comma c equals Lim subscript x not stretchy rightwards arrow 0 end subscript f left parenthesis x right parenthesis$ then

only 'a' exists
b=1
a and c does not exist
None of a,b,c exists

The correct answer is: None of a,b,c exists

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a equals Lim subscript x not stretchy rightwards arrow 0 to the power of minus end subscript f left parenthesis x right parenthesis equals 0 to the power of fraction numerator 1 over denominator negative 1 end fraction end exponent equals 1 over 0 equals text undefined end text semicolon b end cell row cell equals Lim subscript x not stretchy rightwards arrow 0 to the power of plus end subscript f left parenthesis x right parenthesis equals 1 to the power of 1 over 0 end exponent end cell row cell equals text undefined end text end cell end table$

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