Question Number 134843 by Raxreedoroid last updated on 07/Mar/21 $$\mathrm{what}\:\mathrm{is}\:{f}\left({x}\right)? \\ $$$$\mathrm{such}\:\mathrm{that}\:\frac{{f}\left({x}\right)}{{x}}+{f}\:'\left({x}\right)\mathrm{ln}\:{x}=\mathrm{0} \\ $$ Commented by PRITHWISH SEN 2 last updated on 07/Mar/21 $$\frac{\mathrm{C}}{\mathrm{lnx}}\:\:\left(\mathrm{C}=\:\mathrm{constant}\right) \\…
Question Number 134809 by liberty last updated on 07/Mar/21 $${Show}\:{if}\:{f}\:''\left({a}\right)\:{exist}\:{then}\: \\ $$$${f}\:''\left({a}\right)=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{f}\left({a}+{h}\right)+{f}\left({a}−{h}\right)−\mathrm{2}{f}\left({a}\right)}{{h}^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 3707 by Filup last updated on 19/Dec/15 $$\mathrm{lets}\:\mathrm{say}\:\mathrm{we}\:\mathrm{have}\:\mathrm{a}\:\mathrm{function}\:{f}\left({x}\right). \\ $$$$\mathrm{The}\:\mathrm{tangent}\:\mathrm{line}\:\mathrm{at}\:{x}={n}\:\mathrm{makes}\:\mathrm{an} \\ $$$$\mathrm{angle}\:\theta\:\mathrm{with}\:\mathrm{the}\:{x}−\mathrm{axis}. \\ $$$$ \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{change}\:\mathrm{of}\:\mathrm{the}\:\mathrm{angle} \\ $$$$\mathrm{as}\:\mathrm{we}\:\mathrm{change}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}? \\ $$$$ \\ $$$$\mathrm{Suppose}\:{f}\left({x}\right)={x}^{\mathrm{2}} \\…
Question Number 69211 by Mikael last updated on 21/Sep/19 $${To}\:{conserve}\:{rice}\:{from}\:{a}\:{cooperative}\:{there}\:{is} \\ $$$${a}\:{foil}\:{of}\:{area}\:{A}=\mathrm{24}{cm}^{\mathrm{2}} .\:{The}\:{cooperatives} \\ $$$${want}\:{to}\:{build}\:{a}\:{barn}\:{in}\:{the}\:{shape}\:{of}\:{a}\:{parallelopiped} \\ $$$${square}\:{rectangle}\:{without}\:{cover}. \\ $$$${What}\:{should}\:{be}\:{the}\:{symmetrical}\:{dimensions}\:{for} \\ $$$${the}\:{volume}\:{to}\:{be}\:{maximum}? \\ $$ Terms of…
Question Number 134662 by mnjuly1970 last updated on 06/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{nice}\:\:{calculus}… \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\boldsymbol{\phi}=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\zeta\left(\mathrm{2}{n}\right)}{\left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:…{m}.{n}… \\ $$ Answered by Dwaipayan Shikari last…
Question Number 69046 by Rio Michael last updated on 18/Sep/19 Commented by mathmax by abdo last updated on 18/Sep/19 $$\left.\mathrm{4}\right){we}\:{have}\:\:{y}={xarctanx}\:\Rightarrow{y}^{'} ={arctanx}\:+\frac{{x}}{\mathrm{1}+{x}^{\mathrm{2}} }\:\Rightarrow \\ $$$$\left({x}+{x}^{\mathrm{3}} \right){y}^{'}…
Question Number 3417 by RasheedSindhi last updated on 13/Dec/15 $${prove}\:{that}\:{among}\:{all}\:{closed}\:{figures} \\ $$$${having}\:{same}\:{perimeter}\:{circle} \\ $$$${has}\:{maximum}\:{area}. \\ $$ Commented by Filup last updated on 13/Dec/15 $$\mathrm{I}\:\mathrm{dont}\:\mathrm{understand}\:\mathrm{the}\:\mathrm{question} \\…
Question Number 134460 by bramlexs22 last updated on 04/Mar/21 $$ \\ $$2. When the cost of a bag of potatoes is $5 a supermarket sells…
Question Number 3370 by Filup last updated on 12/Dec/15 $${y}={ax}^{{n}} \\ $$$${y}+\delta{y}={a}\left({x}+\delta{x}\right)^{{n}} \\ $$$$\vdots \\ $$$$\frac{{dy}}{{dx}}={a}\underset{\delta{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left({x}+\delta{x}\right)^{{n}} −{x}^{{n}} }{\delta{x}} \\ $$$$ \\ $$$$\mathrm{Show}\:\mathrm{that}\:\frac{{dy}}{{dx}}={anx}^{{n}−\mathrm{1}} \\ $$…
Question Number 134442 by mnjuly1970 last updated on 03/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{nice}\:…..\:{calculus}… \\ $$$$\:\:\:\:{prove}\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{4}} }\right)=\frac{{cosh}\left(\mathrm{2}\pi\right)−{cos}\left(\mathrm{2}\pi\right)}{\mathrm{4}\pi^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:………………….. \\ $$ Answered by Dwaipayan…