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Question Number 40457    Answers: 1   Comments: 0

Question Number 40442    Answers: 2   Comments: 0

Solve : y^4 dx + 2xy^3 dy = ((ydx− xdy)/(x^3 y^3 )).

$$\mathrm{Solve}\:: \\ $$$$\mathrm{y}^{\mathrm{4}} \mathrm{d}{x}\:+\:\mathrm{2}{x}\mathrm{y}^{\mathrm{3}} \mathrm{dy}\:=\:\frac{\mathrm{yd}{x}−\:{x}\mathrm{dy}}{{x}^{\mathrm{3}} \mathrm{y}^{\mathrm{3}} }. \\ $$

Question Number 40434    Answers: 0   Comments: 3

prove that ln(x) is irrational for x natural

$${prove}\:{that}\:\mathrm{ln}\left({x}\right)\:{is}\:{irrational}\:{for}\:{x}\:{natural} \\ $$

Question Number 40426    Answers: 0   Comments: 0

Question Number 40422    Answers: 1   Comments: 1

Solve: ydx − xdy +log xdx =0

$$\mathrm{Solve}: \\ $$$$\mathrm{yd}{x}\:−\:{xdy}\:+\mathrm{log}\:{xdx}\:=\mathrm{0} \\ $$

Question Number 40418    Answers: 2   Comments: 1

Question Number 40417    Answers: 0   Comments: 0

Question Number 40407    Answers: 1   Comments: 0

let f(x)= x^3 −x−1 1) prove that ∃ α ∈ ]1,2[ /f(α)=0 2) use the newton method with x_0 =(3/2) to find a better value for α (take onlly 5 terms)

$${let}\:{f}\left({x}\right)=\:{x}^{\mathrm{3}} −{x}−\mathrm{1} \\ $$$$\left.\mathrm{1}\left.\right)\:{prove}\:{that}\:\exists\:\alpha\:\in\:\right]\mathrm{1},\mathrm{2}\left[\:/{f}\left(\alpha\right)=\mathrm{0}\right. \\ $$$$\left.\mathrm{2}\right)\:{use}\:{the}\:{newton}\:{method}\:\:{with}\:{x}_{\mathrm{0}} =\frac{\mathrm{3}}{\mathrm{2}} \\ $$$${to}\:{find}\:{a}\:{better}\:{value}\:{for}\:\alpha\:\left({take}\:{onlly}\:\mathrm{5}\:{terms}\right) \\ $$

Question Number 40406    Answers: 1   Comments: 0

Question Number 40399    Answers: 3   Comments: 0

Solve : (2(√(xy)) −x)dy + ydx = 0.

$$\mathrm{Solve}\:: \\ $$$$\left(\mathrm{2}\sqrt{{xy}}\:−{x}\right){dy}\:+\:{ydx}\:=\:\mathrm{0}. \\ $$

Question Number 40397    Answers: 1   Comments: 0

Solve : (dy/dx) = ((sin y + x)/(sin 2y − xcos y)) .

$$\mathrm{Solve}\:: \\ $$$$\frac{\mathrm{dy}}{{dx}}\:=\:\frac{\mathrm{sin}\:{y}\:+\:{x}}{\mathrm{sin}\:\mathrm{2}{y}\:−\:{x}\mathrm{cos}\:{y}}\:. \\ $$

Question Number 40396    Answers: 0   Comments: 1

A block lying on a horizontal conv− eyor belt moving at a constant velocity receives a velocity 5m/s at t=0 sec. relative to the ground in the direction opposite to the dir− ction of motion of the conveyor. Aftert=4sec,the velocity of the block becomes equal to the velocity of the belt . the coefficient of friction between the block and the belt is 0.2 . then the velocity of the conveyor belt is: (g=10m/s^2 ) (A) 13 m/s (B) −13m/s (C)3m/s (D) 6m/s

$${A}\:{block}\:{lying}\:{on}\:{a}\:{horizontal}\:{conv}− \\ $$$${eyor}\:{belt}\:{moving}\:{at}\:\:{a}\:{constant}\: \\ $$$${velocity}\:{receives}\:{a}\:{velocity}\:\mathrm{5}{m}/{s} \\ $$$${at}\:{t}=\mathrm{0}\:{sec}.\:{relative}\:{to}\:{the}\:{ground}\: \\ $$$${in}\:{the}\:{direction}\:{opposite}\:{to}\:{the}\:{dir}− \\ $$$${ction}\:{of}\:{motion}\:{of}\:{the}\:{conveyor}. \\ $$$${Aftert}=\mathrm{4}{sec},{the}\:{velocity}\:{of}\:{the}\: \\ $$$${block}\:{becomes}\:{equal}\:{to}\:{the}\:{velocity} \\ $$$${of}\:{the}\:{belt}\:.\:{the}\:{coefficient}\:{of}\: \\ $$$${friction}\:{between}\:{the}\:{block}\:{and}\:{the} \\ $$$${belt}\:{is}\:\mathrm{0}.\mathrm{2}\:.\:{then}\:{the}\:{velocity}\:{of}\:{the} \\ $$$${conveyor}\:{belt}\:{is}:\:\:\left({g}=\mathrm{10}{m}/{s}^{\mathrm{2}} \right) \\ $$$$\left({A}\right)\:\mathrm{13}\:{m}/{s}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({B}\right)\:\:−\mathrm{13}{m}/{s} \\ $$$$\left({C}\right)\mathrm{3}{m}/{s}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({D}\right)\:\:\:\mathrm{6}{m}/{s} \\ $$

Question Number 40388    Answers: 1   Comments: 0

Question Number 40378    Answers: 1   Comments: 3

(1/(1!))+(1/(2!))+(1/(3!))+....+(1/(2018!))=?

$$\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}}{\mathrm{2}!}+\frac{\mathrm{1}}{\mathrm{3}!}+....+\frac{\mathrm{1}}{\mathrm{2018}!}=? \\ $$

Question Number 40376    Answers: 0   Comments: 3

Question Number 40375    Answers: 1   Comments: 0

Question Number 40380    Answers: 2   Comments: 1

Solve : (dy/dx) = ((x+y)/(x−y))

$${S}\mathrm{olve}\::\:\:\:\:\:\frac{\mathrm{dy}}{\mathrm{d}{x}}\:=\:\frac{{x}+{y}}{{x}−{y}} \\ $$

Question Number 40370    Answers: 0   Comments: 1

let u_n =Σ_(k=0) ^n (3k+1)(−1)^k 1) calculate interms of n S_n =u_0 +u_1 +u_2 +....+u_n 2) calculate u_0 +u_1 +u_2 +....+u_(57)

$${let}\:{u}_{{n}} \:=\sum_{{k}=\mathrm{0}} ^{{n}} \left(\mathrm{3}{k}+\mathrm{1}\right)\left(−\mathrm{1}\right)^{{k}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{interms}\:{of}\:{n} \\ $$$${S}_{{n}} ={u}_{\mathrm{0}} \:+{u}_{\mathrm{1}} +{u}_{\mathrm{2}} +....+{u}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{u}_{\mathrm{0}} \:+{u}_{\mathrm{1}} +{u}_{\mathrm{2}} +....+{u}_{\mathrm{57}} \\ $$

Question Number 40466    Answers: 1   Comments: 5

Q..cos^(−1) (1−2x^2 )=2sin^(−1) x,prove please

$$ \\ $$$$ \\ $$$$ \\ $$$${Q}..\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{1}−\mathrm{2}{x}^{\mathrm{2}} \right)=\mathrm{2sin}^{−\mathrm{1}} {x},{prove}\:\:\: \\ $$$${please} \\ $$$$ \\ $$$$ \\ $$

Question Number 40366    Answers: 0   Comments: 1

use newton raphson method to approximate the positive root x^2 −1=0 correct to 4 decimal places perform 3 iteration only setting with x=2

$$\boldsymbol{\mathrm{use}}\:\boldsymbol{\mathrm{newton}}\:\boldsymbol{\mathrm{raphson}}\:\boldsymbol{\mathrm{method}} \\ $$$$\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{approximate}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{positive}}\:\boldsymbol{\mathrm{root}} \\ $$$$\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{1}=\mathrm{0}\:\boldsymbol{\mathrm{correct}}\:\boldsymbol{\mathrm{to}}\:\mathrm{4}\:\boldsymbol{\mathrm{decimal}}\:\boldsymbol{\mathrm{places}} \\ $$$$\boldsymbol{\mathrm{perform}}\:\mathrm{3}\:\boldsymbol{\mathrm{iteration}}\:\boldsymbol{\mathrm{only}} \\ $$$$\boldsymbol{\mathrm{setting}}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{{x}}=\mathrm{2} \\ $$

Question Number 40355    Answers: 1   Comments: 0

Question Number 40352    Answers: 0   Comments: 1

If A= [((4 −3)),((1 0)) ]use the fact that A^2 =4A−3I_2 and mathematical induction to prove A^n =(((3^n −1))/2)A +((3−3^n )/2)I if n≥1

$${If}\:{A}=\begin{bmatrix}{\mathrm{4}\:\:\:\:\:−\mathrm{3}}\\{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\mathrm{0}}\end{bmatrix}{use}\:{the}\:{fact}\:{that}\: \\ $$$${A}^{\mathrm{2}} =\mathrm{4}{A}−\mathrm{3}{I}_{\mathrm{2}} \:\:{and}\:{mathematical}\:{induction}\:{to}\:{prove} \\ $$$$\:\:{A}^{{n}} =\frac{\left(\mathrm{3}^{{n}} −\mathrm{1}\right)}{\mathrm{2}}{A}\:\:+\frac{\mathrm{3}−\mathrm{3}^{{n}} }{\mathrm{2}}{I}\:\:{if}\:{n}\geqslant\mathrm{1} \\ $$

Question Number 40467    Answers: 1   Comments: 2

∫ln ∣(√(x+1))+(√x)∣ dx=

$$\int\mathrm{ln}\:\mid\sqrt{{x}+\mathrm{1}}+\sqrt{{x}}\mid\:{dx}= \\ $$

Question Number 40344    Answers: 1   Comments: 2

Question Number 40322    Answers: 1   Comments: 4

Solve : (d^2 y/dx^2 ) = ((dy/dx))^2

$$\mathrm{Solve}\:: \\ $$$$\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{d}{x}^{\mathrm{2}} }\:=\:\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} \\ $$

Question Number 40321    Answers: 0   Comments: 1

If abc=8 and (1/a) + (1/b) + (1/c) = (3/2) then find the value of ab+bc+ca.

$$\mathrm{If}\:{abc}=\mathrm{8}\:\mathrm{and}\:\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}}\:=\:\frac{\mathrm{3}}{\mathrm{2}}\:\mathrm{then} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:{ab}+{bc}+{ca}. \\ $$

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