1.

Examine the continuity of the following functions at indicated points.f(x)={((1+2x)^(1/2)if xne0),(e^2 if x=0at x=0):}

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Solution :We KNOW that a function F(x) is CONTINUOUS at a point x=a
if `LIM(xtoa)f(x)=f(a)`
Now `lim_(xto0)f(x)=lim_(xto0)(1+2x)^(1/x)=e^2`
Again `f(0)=e^2`
THUS `lim_(xto0)f(x)=f(0)`
So f(x) is continuous at x=0


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