Question

$\underset{x\to 0^{+}}{lim}(\left(x^{x^x}\right)-x^x)$ is

• A. Equal to 0
• B. Equal to 1
• C. Equal to -1
• D. Non existent

Answer 1

The correct option is C Equal to -1

$\underset{x\to 0^{+}}{lim}\left\{\right(x^{x^x})-x^x\}=\underset{x\to 0^{+}}{lim}\left(x^{x^x}\right)-\underset{x\to 0^{+}}{lim}{x}^x=\underset{x\to 0^{+}}{lim}\left(x^{x^{\underset{x\to 0^{+}}{lim}x}}\right)-\underset{x\to 0^{+}}{lim}{x}^{\underset{x\to 0^{+}}{lim}x}=\underset{x\to 0^{+}}{lim}\left(x\right)-1=-1$