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Mathematics : Continuity and Differentiability

Long Answer Type

111. Find all points of discontinuity of f, where f is defined by

straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator open vertical bar straight x close vertical bar over denominator straight x end fraction comma space space space space if space straight x not equal to 0 end cell row cell 0 comma space space space space space space space space space if space straight x equals 0 end cell end table close

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112. Find all points of discontinuity of f, where f is defined by

straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator straight x over denominator open vertical bar straight x close vertical bar end fraction comma space if space straight x less than 0 end cell row cell space minus 1 comma space space if space straight x greater or equal than 0 end cell end table close

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113.

Find all points of discontinuity of f, where f is defined by
$straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell space straight x plus 1 comma space if space straight x greater or equal than 1 end cell row cell straight x squared plus 1 comma space if space straight x less than 1 end cell end table close$

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114.

Find all points of discontinuity of f, where f is defined by
$straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell straight x cubed minus 3 comma space if space straight x less or equal than 2 end cell row cell straight x squared plus 1 comma space if space straight x greater than 2 end cell end table close$

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115.

Find all points of discontinuity of f, where f is defined by
$straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell straight x to the power of 10 minus 1 comma space space if space straight x less or equal than 1 end cell row cell straight x squared comma space space space space space space space space space space space if space straight x greater than 1 end cell end table close$