Question Number 170057 by nimnim last updated on 15/May/22 | ||
$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{{x}}{{a}}\lfloor\frac{{b}}{{x}}\rfloor\:\:{where}\:{a},{b}>\mathrm{0} \\ $$ $${please}.... \\ $$ | ||
Answered by mahdipoor last updated on 15/May/22 | ||
$${get}\:\frac{{b}}{{x}}={t}\:\: \\ $$ $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}}{{a}}\left[\frac{{b}}{{x}}\right]=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{b}}{{a}}×\frac{\left[\frac{{b}}{{x}}\right]}{\frac{{b}}{{x}}}=\frac{{b}}{{a}}\underset{{t}\rightarrow\pm\infty} {\mathrm{lim}}\frac{\left[{t}\right]}{{t}}=\frac{{b}}{{a}} \\ $$ | ||