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Examine the continuity of the following ...

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

Text Solution

Verified by Experts

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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