f-x-x-sin-1-x-if-0-lt-x-1-0-if-x-0-Show-that-f-is-continous-but-not-of-bounded-variation-

Question Number 152362 by Tawa11 last updated on 27/Aug/21

f (x) = {\begin{cases} x \sin \frac{1}{x}, if 0 < x ⩽ 1 \\ 0, if x = 0 \end{cases}

Show that f is continous but not of bounded variation