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Examine the continuity of the function f(x) =sin x- cos x, for x ≠ 0 ,=- 1 ,for x=0 at the poinl x = 0 - Mathematics and Statistics

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Examine the continuity of the function
f(x) =sin x- cos x, for x ≠ 0

      =- 1 ,forx=0

at the poinl x = 0

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Solution

`f(0)=-1`

`and lim_(x->0)f(x)`

`=lim_(x->0)(sinx-cosx)=-1`

`therefore f(0)=lim_(x->0)f(x)`

Hence f (x)  is continuous at x = 0

Concept: Introduction of Continuity
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