Question Number 141417 by mnjuly1970 last updated on 18/May/21 $$\:\:\:\:\:\:\:\:\:\:……..\:{advanced}\:…\:…\:…\:{calculus}……. \\ $$$$\:\:\:\:{prove}\:{that}:: \\ $$$$\:\:\:\:\:\mathscr{F}:=\:\int_{−\mathrm{1}} ^{\:\mathrm{0}} \frac{{e}^{{x}} +{e}^{\frac{\mathrm{1}}{{x}}} −\mathrm{1}}{{x}}\:{dx}\overset{??} {=}\gamma \\ $$ Answered by mnjuly1970 last…
Question Number 10347 by konen last updated on 04/Feb/17 $$\mathrm{A}=\mathrm{1}+\mathrm{2}+\mathrm{3}+…+\mathrm{n}−\mathrm{2} \\ $$$$\mathrm{B}=\mathrm{15}+\mathrm{16}+…..+\mathrm{n} \\ $$$$\mathrm{A}−\mathrm{B}=\mathrm{42}\Rightarrow\mathrm{n}=? \\ $$ Answered by mrW1 last updated on 05/Feb/17 $${A}=\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{2}}…
Question Number 75883 by TawaTawa last updated on 19/Dec/19 $$\mathrm{If}\:\:\:\:\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} \:+\:\mathrm{c}^{\mathrm{4}} \:+\:\mathrm{d}^{\mathrm{4}} \:\:\:=\:\:\:\mathrm{16} \\ $$$$\mathrm{Prove}\:\mathrm{that},\:\:\:\:\:\:\:\:\mathrm{a}^{\mathrm{5}} \:+\:\mathrm{b}^{\mathrm{5}} \:+\:\mathrm{c}^{\mathrm{5}} \:+\:\mathrm{d}^{\mathrm{5}} \:\:\:\leqslant\:\:\:\mathrm{32} \\ $$ Commented by prakash…
Question Number 141419 by mnjuly1970 last updated on 18/May/21 $$ \\ $$$$\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left({cosh}\left({x}\right)\right)}{{cosh}\left({x}\right)}{dx}\overset{?} {=}\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {log}\left(\frac{\mathrm{1}}{{sin}\left({x}\right)}\right){dx} \\ $$ Answered by mindispower last updated on…
Question Number 141413 by Willson last updated on 18/May/21 $$\underset{\:\mathrm{1}} {\int}^{\:+\infty} \left(\frac{\mathrm{1}}{\mathrm{E}\left(\mathrm{x}\right)}−\frac{\mathrm{1}}{\mathrm{x}}\right)\mathrm{dx}=??? \\ $$ Answered by Mathspace last updated on 18/May/21 $$=\sum_{{n}=\mathrm{1}} ^{\infty\:} \int_{{n}} ^{{n}+\mathrm{1}}…
Question Number 141412 by bramlexs22 last updated on 18/May/21 $$\:{Find}\:{the}\:{range}\:{of}\:{real}\:{number} \\ $$$${of}\:{q}\:{such}\:{that}\:{the}\:{function}\: \\ $$$$\:{f}\left({x}\right)\:=\:\mathrm{cos}\:{x}\left({q}\:\mathrm{sin}\:^{\mathrm{2}} {x}−\mathrm{5}\right)\:{have} \\ $$$${minimum}\:{value}\:{is}\:−\mathrm{5}\:. \\ $$ Commented by MJS_new last updated on…
Question Number 75879 by TawaTawa last updated on 19/Dec/19 Answered by mr W last updated on 19/Dec/19 Commented by mr W last updated on 19/Dec/19…
Question Number 141414 by bekzodjumayev last updated on 18/May/21 Commented by bekzodjumayev last updated on 18/May/21 $${Help}? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 10340 by konen last updated on 04/Feb/17 $$\mathrm{A}=\mathrm{1}×\mathrm{2}\:+\mathrm{2}×\mathrm{4}\:+\mathrm{3}×\mathrm{6}+…+\mathrm{14}×\mathrm{28} \\ $$$$\mathrm{B}=\mathrm{1}×\mathrm{3}\:+\mathrm{2}×\mathrm{3}\:+…+\mathrm{14}×\mathrm{29} \\ $$$$\Rightarrow\mathrm{B}=? \\ $$ Commented by mrW1 last updated on 04/Feb/17 $${the}\:{definition}\:{of}\:{B}\:{is}\:{not}\:{clear}. \\…
Question Number 141409 by Willson last updated on 18/May/21 $$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\forall\mathrm{n}\in\mathbb{N}\:\:\:\:\underset{\mathrm{n}} {\int}^{\:\mathrm{n}+\mathrm{1}} \mathrm{lnt}\:\mathrm{dt}\:\leqslant\:\mathrm{ln}\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$ Answered by TheSupreme last updated on 19/May/21 $$\int{ln}\left({t}\right)={xln}\left({t}\right)−{x} \\…