Question

In order that the function $f\left(x\right)=(x+1{)}^{\frac{1}{x}}$ is continuous at x = 0; f(0) must be defined as

• A. f(0) = 0
• B. f(0) = e
• C. $f\left(0\right)=\frac{1}{e}$
• D. f(0) = 1

Answer 1

The correct option is B f(0) = e

${lim}_{x\to 0}f\left(x\right)=f\left(0\right){lim}_{x\to 0}(0+x{)}^{\frac{1}{x}}=e$
So, f(0) = e