Question

$\underset{x\to 0}{lim}\frac{\log x^n-\left[x\right]}{\left[x\right]}$, $nϵN$ denotes greatest integer less than or equal to x

• A. has value -1
• B. has value 0
• C. has value 1
• D. does not exist

Answer 1

The correct option is D does not exist

$\underset{x\to 0}{lim}\frac{\log x^n-\left[x\right]}{\left[x\right]}$

$={lim}_{x\to 0}\frac{n\log x}{\left[x\right]}-1$ which does not exist as $\underset{x\to 0}{lim}\frac{\log x}{\left[x\right]}$ does not exist.