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Examine the continuity of the following functions at indicated points.f(x)={((sin2x)/x if xne0 at x=0),(2 if x=0):} |
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Answer» Solution :`lim_(xto0)f(x)=lim_(xto0)(sin2x)/x` `lim_(xto0)2 cdot (sin2x)/(2X)=2 cdot lim_(2xto0)(sin2x)/(2x)=2 cdot 1` `=2(becauselim_(theta=0)(sintheta)/theta=1)` Again `f(0)=2implieslim_(xto0)f(x)=f(0)` `THEREFORE` The function f(x) is CONTINUOUS at x=0 |
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