Use continuity to evaluate the limit. limx→πsin⁡(x+sin⁡x)

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x and sin⁡x are continuous, therefore x+sin⁡x is continuous  Recall that : f(g(x)) is continuous if f(x) and g(x) are continuous  Therefore sin⁡(x+sin⁡x) is a continuous function  Recall that : If f(x) is continuous at x=a, then limx→af(x)=f(a)  Therefore  limx→πsin⁡(x+sin⁡x)=sin⁡(π+sin⁡π)=sin⁡(π+0)=sin⁡π=0  Result:  limx→πsin⁡(x+sin⁡x)=0

Use continuity to evaluate the limit. limx→πsin⁡(x+sin⁡x)

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