Menu Close

Category: Differentiation

Question-126854

Question Number 126854 by sdfg last updated on 24/Dec/20 Answered by mathmax by abdo last updated on 24/Dec/20 $$\mathrm{h}\rightarrow\mathrm{r}^{\mathrm{2}} \:+\mathrm{k}^{\mathrm{2}} =\mathrm{0}\:\Rightarrow\mathrm{r}^{\mathrm{2}} =−\mathrm{k}^{\mathrm{2}} \:\Rightarrow\mathrm{r}\:=\overset{−} {+}\mathrm{ik}\:\Rightarrow\mathrm{y}_{\mathrm{h}} =\mathrm{ae}^{\mathrm{ikx}}…

Find-minimum-value-of-y-1-sin-2-x-2-tan-2-x-

Question Number 192343 by cortano12 last updated on 15/May/23 $$\:\mathrm{Find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\:\:\:\:\:\:\mathrm{y}=\frac{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{2}\:\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}\: \\ $$ Answered by manxsol last updated on 15/May/23 $$\:\:{x}\neq{k}\pi\frac{\pi}{\mathrm{2}}\:\:\:\:{y}>\mathrm{0} \\…

let-consider-u-n-such-as-u-0-0-1-and-u-n-1-u-n-u-n-2-1-Prove-that-lim-n-n-u-n-1-and-that-the-convergence-domain-of-u-n-x-n-is-D-1-1-2-Prove-that-the-one-of-u-n-2-x-n

Question Number 126777 by snipers237 last updated on 24/Dec/20 $$\left.{let}\:{consider}\:\left({u}_{{n}} \right)\:{such}\:{as}\:{u}_{\mathrm{0}} \in\right]\mathrm{0};\mathrm{1}\left[\:{and}\:{u}_{{n}+\mathrm{1}} ={u}_{{n}} −{u}_{{n}} ^{\mathrm{2}} \:\right. \\ $$$$\left.\mathrm{1}\right){Prove}\:{that}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:^{{n}} \sqrt{{u}_{{n}} }\:=\:\mathrm{1}\:{and}\:{that}\:{the}\:{convergence}\:{domain}\:{of}\:\Sigma{u}_{{n}} {x}^{{n}} \: \\ $$$${is}\:\:{D}=\left[−\mathrm{1};\mathrm{1}\left[\:\right.\right.…

e-e-sin-x-sec-2-x-1-dx-

Question Number 192289 by cortano12 last updated on 14/May/23 $$\:\:\:\:\:\:\:\:\underset{−\mathrm{e}} {\overset{\mathrm{e}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}+\mathrm{1}}\:\mathrm{dx}\:=? \\ $$ Answered by mehdee42 last updated on 14/May/23 $${f}\left({x}\right)=\frac{{sinx}}{{secx}^{\mathrm{2}} {x}+\mathrm{1}}\Rightarrow{f}\left(−{x}\right)={f}\left({x}\right) \\…

advanced-calculus-prove-that-n-1-H-n-n-4-3-5-2-3-where-H-n-1-1-2-1-3-1-n-

Question Number 126726 by mnjuly1970 last updated on 23/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:{calculus}… \\ $$$$\:\:{prove}\:\:{that}\::\: \\ $$$$\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}\:} {\overset{\infty} {\sum}}\frac{\mathrm{H}_{{n}} }{{n}^{\mathrm{4}} }\:\overset{?} {=}\mathrm{3}\zeta\left(\mathrm{5}\right)−\zeta\left(\mathrm{2}\right)\left(\mathrm{3}\right)\:\:…. \\ $$$$\:\:\:{where}::\:\:\:\:\mathrm{H}_{{n}\:} \:=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}\:+…+\frac{\mathrm{1}}{{n}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:………. \\…