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Category: Differentiation

put-gcd-a-b-a-b-if-a-b-a-c-b-c-1-prove-that-abc-ab-ac-bc-1-

Question Number 163271 by mnjuly1970 last updated on 05/Jan/22 $$ \\ $$$$\:\:\:\:\:\:{put}\::\:\:{gcd}\left(\:{a}\:,\:{b}\:\right)=\:\left({a},\:{b}\:\right) \\ $$$$\:\:\:\:\:\:\:{if}\:\:\:\left(\:{a}\:,{b}\:\right)=\:\left({a}\:,{c}\:\right)=\:\left({b}\:,{c}\:\right)=\mathrm{1} \\ $$$${prove}\:{that}\::\:\:\left({abc}\:,\:{ab}\:+{ac}\:+{bc}\:\right)=\mathrm{1} \\ $$$$ \\ $$ Terms of Service Privacy Policy…

prove-or-disprove-2pi-4pi-sin-x-x-dx-gt-0-because-2pi-3pi-sin-x-x-dx-gt-3pi-4pi-sin-x-x-dx-

Question Number 163134 by mnjuly1970 last updated on 04/Jan/22 $$ \\ $$$$\:\:\:\:{prove}\:\:{or}\:{disprove} \\ $$$$ \\ $$$$\:\:\:\:\int_{\mathrm{2}\pi} ^{\:\mathrm{4}\pi} \frac{\:{sin}\left({x}\right)}{{x}}\:{dx}\:>\mathrm{0} \\ $$$$\:\:\:\:\:\:\:{because} \\ $$$$\:\int_{\mathrm{2}\pi} ^{\:\mathrm{3}\pi} \frac{\:{sin}\left({x}\:\right)}{{x}}\:{dx}\:>\:\int_{\mathrm{3}\pi} ^{\:\mathrm{4}\pi}…

F-x-x-2-4x-2-1-3-local-maximum-absolut-maximum-

Question Number 163080 by tounghoungko last updated on 03/Jan/22 $$\:\:\:\:\:\:\:{F}\left({x}\right)=\:\sqrt[{\mathrm{3}}]{\left({x}^{\mathrm{2}} −\mathrm{4}{x}\right)^{\mathrm{2}} }\: \\ $$$$\:\:\left.\begin{matrix}{{local}\:{maximum}}\\{{absolut}\:{maximum}}\end{matrix}\right\}\:=? \\ $$ Answered by mahdipoor last updated on 03/Jan/22 $${F}\:'=\frac{\mathrm{2}}{\mathrm{3}}\left({x}^{\mathrm{2}} −\mathrm{4}{x}\right)^{\frac{−\mathrm{1}}{\mathrm{3}}}…

prove-that-n-1-2n-1-2n-1-2-n-2n-1-2-pi-2-4-1-

Question Number 163045 by mnjuly1970 last updated on 03/Jan/22 $$ \\ $$$$\:\:\:\:\:{prove}\:{that} \\ $$$$ \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\left(\:\mathrm{2}{n}+\mathrm{1}\:\right)!!}{\left(\mathrm{2}{n}\:\right)!!}\:\frac{\mathrm{1}}{\mathrm{2}^{\:{n}} \left(\mathrm{2}{n}\:+\mathrm{1}\right)^{\:\mathrm{2}} }\:=\frac{\pi\sqrt{\mathrm{2}}}{\mathrm{4}}−\mathrm{1} \\ $$ Answered by qaz…

0-x-sin-x-x-3-dx-solution-I-B-P-1-2-x-2-x-sin-x-0-1-2-0-1-cos-x-x-2-dx-1-2-0-2sin-2-

Question Number 163033 by mnjuly1970 last updated on 03/Jan/22 $$ \\ $$$$\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{x}\:−\:{sin}\:\left({x}\:\right)}{{x}^{\:\mathrm{3}} }{dx} \\ $$$$−−−\:{solution}−−− \\ $$$$\:\:\:\:\:\Omega\overset{\mathscr{I}.\mathscr{B}.\mathscr{P}} {=}\:\left[\:\frac{−\mathrm{1}}{\mathrm{2}\:{x}^{\:\mathrm{2}} }\:\left({x}−{sin}\left({x}\right)\right)\right]_{\mathrm{0}} ^{\infty} +\frac{\mathrm{1}}{\mathrm{2}}\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}−{cos}\:\left({x}\right)}{{x}^{\:\mathrm{2}}…

In-each-week-the-growth-of-a-plant-is-two-thirds-the-growth-of-the-previous-week-The-plant-grows-12-cm-in-the-first-week-a-Calculate-the-growth-of-the-plant-in-b-the-limiting-height-of-the-pant

Question Number 97483 by Rio Michael last updated on 08/Jun/20 $$\mathrm{In}\:\mathrm{each}\:\mathrm{week}\:\mathrm{the}\:\mathrm{growth}\:\mathrm{of}\:\mathrm{a}\:\mathrm{plant}\:\mathrm{is}\:\mathrm{two}−\mathrm{thirds} \\ $$$$\mathrm{the}\:\mathrm{growth}\:\mathrm{of}\:\mathrm{the}\:\mathrm{previous}\:\mathrm{week}. \\ $$$$\mathrm{The}\:\mathrm{plant}\:\mathrm{grows}\:\mathrm{12}\:\mathrm{cm}\:\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{week}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{growth}\:\mathrm{of}\:\mathrm{the}\:\mathrm{plant}\:\mathrm{in}\: \\ $$$$\left(\mathrm{b}\right)\:\mathrm{the}\:\mathrm{limiting}\:\mathrm{height}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pant} \\ $$ Commented by bobhans last…