Question 11

Calculus Level 4

The value of $\lim_{x\rightarrow 0^{+}}(1+\lfloor x \rfloor)^{1/x}$ is :

$\text{Details and Assumptions:}$

$\bullet$ $\lfloor x \rfloor$ is the greatest integer $\leq x$

$\bullet$ This question is part of the set For the JEE-nius;P

Doesn't exist 0 e 1

1 solution

Andrea Palma
Jun 16, 2015

In a right neighborough of $0$ , we have $\lfloor x \rfloor = 0$ . So the function near $0$ is in fact $1^{1/x}$ that is constant $1$ .