Question Number 142140 by gsk2684 last updated on 26/May/21 $$\left[\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:{x}}{{x}}\right]=? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\left[\frac{\mathrm{100sin}^{−\mathrm{1}} {x}}{{x}}\right]+\left[\frac{\mathrm{100tan}^{−\mathrm{1}} {x}}{{x}}\right]\right\}=? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\left[\frac{\mathrm{100}{x}}{\mathrm{sin}^{−\mathrm{1}} {x}}\right]+\left[\frac{\mathrm{100}{x}}{\mathrm{tan}^{−\mathrm{1}} {x}}\right]\right\}=? \\ $$$${where}\:\left[{x}\right]\:{denotes}\:{greatest}\:{integer}\: \\ $$$${less}\:{than}\:{or}\:{equal}\:{to}\:{x}.…
Question Number 11036 by suci last updated on 08/Mar/17 $${l}\underset{{n}\rightarrow\sim} {{i}m}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{8}{n}^{\mathrm{2}} }{{n}^{\mathrm{4}} +\mathrm{1}}\:=….? \\ $$ Commented by FilupS last updated on 08/Mar/17 $${S}=\underset{{n}\rightarrow\infty}…
Question Number 142041 by nadovic last updated on 25/May/21 Answered by TheSupreme last updated on 25/May/21 $$\sqrt{−\mathrm{3}{a}+{b}}−\mathrm{2}=\mathrm{0} \\ $$$${b}−\mathrm{3}{a}=\mathrm{4} \\ $$$$\frac{−\mathrm{3}{a}}{\mathrm{2}\sqrt{−\mathrm{3}{a}+{b}}}=−\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\mathrm{6}{a}=\sqrt{−\mathrm{3}{a}+{b}} \\ $$$$\mathrm{36}{a}^{\mathrm{2}}…
Question Number 76445 by john santu last updated on 27/Dec/19 $${how}\:{evaluate}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }×\mathrm{cos}\:{x}}{{x}^{\mathrm{4}} }\right). \\ $$ Commented by JDamian last updated on 27/Dec/19 $${What}\:{if}\:{you}\:{use}\:{L}'{Hopital}'{s}\:{rule}? \\…
Question Number 141964 by gsk2684 last updated on 25/May/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{sin}\:{x}\right)^{\frac{\mathrm{1}}{{x}}} =? \\ $$ Commented by gsk2684 last updated on 25/May/21 $${solution}\:{please} \\ $$ Answered…
Question Number 141965 by gsk2684 last updated on 25/May/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}^{{n}} \mathrm{sin}\:^{{n}} {x}}{{x}^{{n}} −\mathrm{sin}\:^{{n}} {x}}\:{is}\:{non}-{zero}\:{finite},\: \\ $$$${then}\:{find}\:{n}? \\ $$ Commented by gsk2684 last updated on…
Question Number 141961 by iloveisrael last updated on 25/May/21 $$\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{50}} −\mathrm{8}{x}+\mathrm{7}}{{x}^{\mathrm{20}} +\mathrm{5}{x}−\mathrm{6}}\:=? \\ $$ Answered by iloveisrael last updated on 25/May/21 Answered by Panacea…
Question Number 141966 by gsk2684 last updated on 25/May/21 $${find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{log}\:{x}^{{n}} −\left[{x}\right]}{\left[{x}\right]},\:{n}\in{N}\:{where}\: \\ $$$$\left[{x}\right]\:{represents}\:{greatest}\:{integer}\:{less}\:{than}\:{or}\:{equal}\:{to}\:{x}. \\ $$ Commented by gsk2684 last updated on 25/May/21 $${solution}\:{please} \\…
Question Number 141914 by mnjuly1970 last updated on 24/May/21 $$\:\:\:\: \\ $$$$\:\:\:\:\:\:{prove}\:{that}:: \\ $$$$\:\:\:\:\:\phi:=\int_{\mathrm{0}} ^{\:\pi} \frac{{x}}{\left({sin}\left({x}\right)\right)^{\frac{\mathrm{1}}{\mathrm{2}}} }{dx}=\sqrt{\frac{\pi}{\mathrm{8}}}\:\Gamma^{\:\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)…\checkmark \\ $$$$\:\:\:\:\:\:\:\:\:……… \\ $$ Answered by qaz…
Question Number 141901 by gsk2684 last updated on 24/May/21 Commented by gsk2684 last updated on 24/May/21 $${does}\:{this}\:{series}\:{converges}\:{or}\:{diverges} \\ $$$${by}\:{using}\:{comparison}\:{test}\:{or}\:{limit} \\ $$$${comparison}\:{test}?\:{explanation}\:{please} \\ $$ Terms of…