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Here f(x)=cos(x 2 ) Let g(x)= cosx and h(x)=x 2 ∴ (g o h)(x)=g(h(x))=g(x 2 ) =cos x 2 Now f(x)=(g o h)(x) and g.h are both continuous functions ∴ f is continuous function.

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Continuity and Differentiability

Short Answer Type

121.

Find the values of a and b such that the function defined by
$straight f left parenthesis straight x right parenthesis equals open curly brackets table row cell 5 comma end cell row cell ax plus straight b comma end cell row cell 21 comma end cell end table close table row cell if space straight x less or equal than 2 space space space space space space space space space space end cell row cell if space 2 less than straight x less than 10 end cell row cell if space straight x greater or equal than 10 space space space space space space space space end cell end table$
is a continous function.

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122. Show that the function defined by f(x) = sin (x² ) is a continuous function.

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123. Show that the function defined by f(x) = cos(x²) is a continuous function.

Here f(x)=cos(x²)
Let g(x)= cosx and h(x)=x²∴ (g o h)(x)=g(h(x))=g(x²) =cos x²Now f(x)=(g o h)(x) and g.h are both continuous functions
∴ f is continuous function.

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