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  4. In order that the function f(x) = (x + 1)1/x is continuous at x = 0 , f(0) must be defined as

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Q. In order that the function $f(x) = (x + 1)^{1/x} $ is continuous at $x = 0 , f(0)$ must be defined as

BITSATBITSAT 2011

Solution:

$ \displaystyle\lim_{x\to0} f\left(x\right) = f\left(0\right)=\displaystyle \lim _{x\to 0} \left(1+x\right)^{1/x} = e $