Question Number 26142 by moxhix last updated on 21/Dec/17 | ||
$$\mathrm{Prove}\:\mathrm{that}\: \\ $$ $$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{Riemann}\:\mathrm{integrable}\:\mathrm{on}\:\left[{a},{b}\right]\:\mathrm{and} \\ $$ $$\:\:\:\:\:\exists{M}>\mathrm{0}\:{s}.{t}.\:\forall{x}\in\left[{a},{b}\right]\:\left({f}\left({x}\right)\neq\mathrm{0}\:{and}\:\mid{f}\left({x}\right)\mid<{M}\:{and}\:\mid\frac{\mathrm{1}}{{f}\left({x}\right)}\mid<{M}\right), \\ $$ $$\mathrm{then}\:\frac{\mathrm{1}}{{f}\left({x}\right)}\:\mathrm{is}\:\mathrm{Riemann}\:\mathrm{integrable}\:\mathrm{on}\:\left[{a},{b}\right]. \\ $$ | ||