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Continuity and Differentiability
Question
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Show that the function defined by f(x) =  cos(x2) is a continuous function.

Answer

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

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