Answer to Question #197206 in Real Analysis for Dharaba Parmar

Question

Is 1/x^2/3 continuous on [1 2] ?

Answer 1

$\text{Given,} f(x)=\frac{1}{x^\frac{2}{3}}.\newline \text{Since, f is not continuous at x=0 only and}\space x=0 \,\text{is not in the domain [1, 2].}\newline \text{ Therefore, the given function is continuous on\,} [1, 2].$