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Question Number 169447    Answers: 0   Comments: 0

The equation of the curve is given y=(x^3 /6)−((5x^2 )/2)−6x−1 1) Determine the critical points 2) Distinguish between these points 3) Determine the Maximum and minimum values 4) Determine the value of x and y at point of inflexion Mastermind

$${The}\:{equation}\:{of}\:{the}\:{curve}\:{is}\:{given} \\ $$$${y}=\frac{{x}^{\mathrm{3}} }{\mathrm{6}}−\frac{\mathrm{5}{x}^{\mathrm{2}} }{\mathrm{2}}−\mathrm{6}{x}−\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{Determine}\:{the}\:{critical}\:{points} \\ $$$$\left.\mathrm{2}\right)\:{Distinguish}\:{between}\:{these}\:{points} \\ $$$$\left.\mathrm{3}\right)\:{Determine}\:{the}\:{Maximum}\:{and} \\ $$$${minimum}\:{values} \\ $$$$\left.\mathrm{4}\right)\:{Determine}\:{the}\:{value}\:{of}\:{x}\:{and}\:{y} \\ $$$${at}\:{point}\:{of}\:{inflexion}\: \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169445    Answers: 0   Comments: 8

let x and y be positive reals such that x^3 + y^3 + (x+y)^3 +30xy = 2000 show that x+y = 10

$$ \\ $$$$\:\:\:\mathrm{let}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{reals}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:+\:\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{3}} \:+\mathrm{30xy}\:=\:\mathrm{2000} \\ $$$$\:\:\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{x}+\mathrm{y}\:=\:\mathrm{10} \\ $$

Question Number 169439    Answers: 1   Comments: 0

Question Number 169438    Answers: 0   Comments: 1

Question Number 169436    Answers: 1   Comments: 1

Question Number 169429    Answers: 1   Comments: 0

(√(220+30(√(35))))=

$$\sqrt{\mathrm{220}+\mathrm{30}\sqrt{\mathrm{35}}}= \\ $$

Question Number 169421    Answers: 0   Comments: 0

Question Number 169413    Answers: 0   Comments: 0

Question Number 169412    Answers: 0   Comments: 1

Question Number 169407    Answers: 1   Comments: 0

Question Number 169389    Answers: 0   Comments: 1

1. 2(√y) dx = dy 2. (x^2 + y^2 )dx = 2xydy 3. xdx + (1/y) dy = 0 4. dy = 3x^2 dx 5. 2y^2 dx + x(1 + y^2 ) dy = 0 6. 4x^3 dx + dy = 0

$$\mathrm{1}.\:\mathrm{2}\sqrt{\mathrm{y}}\:\mathrm{dx}\:=\:\mathrm{dy} \\ $$$$\mathrm{2}.\:\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \right)\mathrm{dx}\:=\:\mathrm{2xydy} \\ $$$$\mathrm{3}.\:\mathrm{xdx}\:+\:\frac{\mathrm{1}}{\mathrm{y}}\:\mathrm{dy}\:=\:\mathrm{0} \\ $$$$\mathrm{4}.\:\mathrm{dy}\:=\:\mathrm{3x}^{\mathrm{2}} \:\mathrm{dx} \\ $$$$\mathrm{5}.\:\mathrm{2y}^{\mathrm{2}} \mathrm{dx}\:+\:\mathrm{x}\left(\mathrm{1}\:+\:\mathrm{y}^{\mathrm{2}} \right)\:\mathrm{dy}\:=\:\mathrm{0} \\ $$$$\mathrm{6}.\:\mathrm{4x}^{\mathrm{3}} \mathrm{dx}\:+\:\mathrm{dy}\:=\:\mathrm{0} \\ $$

Question Number 169382    Answers: 1   Comments: 7

find the value of [v] if v denotes maximum value of x^2 + y^2 , where (x+5)^2 + (y−12)^2 = 14 (hint [•] repersent greatest integer function of “ •”)

$$\:\:\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\:\left[\boldsymbol{\mathrm{v}}\right]\:\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{v}}\:\boldsymbol{\mathrm{den}{o}\mathrm{tes}}\:\boldsymbol{\mathrm{maximum}}\:\: \\ $$$$\:\:\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:+\:\boldsymbol{\mathrm{y}}^{\mathrm{2}} \:,\:\boldsymbol{\mathrm{where}}\:\left(\boldsymbol{\mathrm{x}}+\mathrm{5}\right)^{\mathrm{2}} \:+\:\left(\boldsymbol{\mathrm{y}}−\mathrm{12}\right)^{\mathrm{2}} \:=\:\mathrm{14} \\ $$$$\:\:\:\:\left(\boldsymbol{\mathrm{hint}}\:\left[\bullet\right]\:\boldsymbol{\mathrm{repersent}}\:\boldsymbol{\mathrm{greatest}}\:\boldsymbol{\mathrm{integer}}\:\boldsymbol{\mathrm{function}}\:\boldsymbol{\mathrm{of}}\:``\:\bullet''\right) \\ $$$$ \\ $$$$\: \\ $$

Question Number 169391    Answers: 1   Comments: 2

Question Number 169396    Answers: 0   Comments: 14

(√x)+1=0 find x Mastermind

$$\sqrt{{x}}+\mathrm{1}=\mathrm{0} \\ $$$${find}\:{x} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169397    Answers: 2   Comments: 0

Question Number 169366    Answers: 0   Comments: 1

Differentiate from first principle y=log_x a Mastermind

$${Differentiate}\:{from}\:{first}\:{principle} \\ $$$${y}={log}_{{x}} {a} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169364    Answers: 1   Comments: 0

Show that the differential equation y′′ −4y′+4y=0 is satisfied when y=xe^(2x) Mastermind

$${Show}\:{that}\:{the}\:{differential}\:{equation} \\ $$$${y}''\:−\mathrm{4}{y}'+\mathrm{4}{y}=\mathrm{0}\:{is}\:{satisfied}\:{when} \\ $$$${y}={xe}^{\mathrm{2}{x}} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169362    Answers: 2   Comments: 0

∫tan(2x+3)dx Mastermind

$$\int{tan}\left(\mathrm{2}{x}+\mathrm{3}\right){dx} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169358    Answers: 1   Comments: 0

Differentiate from first principle y=(1/(x^2 +5))

$${Differentiate}\:{from}\:{first}\:{principle} \\ $$$${y}=\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{5}} \\ $$

Question Number 169356    Answers: 3   Comments: 0

1. y = arcsin(sinx) ⇒ y^′ =? 2. y = sin (√(x + 1)) ⇒ y^′ =? 3. y = ln^5 sinx ⇒ y^′ =? 4. y = cos(2x + 3) ⇒ y^′ =?

$$\mathrm{1}.\:\mathrm{y}\:=\:\mathrm{arcsin}\left(\mathrm{sinx}\right)\:\Rightarrow\:\mathrm{y}^{'} =? \\ $$$$\mathrm{2}.\:\mathrm{y}\:=\:\mathrm{sin}\:\sqrt{\mathrm{x}\:+\:\mathrm{1}}\:\Rightarrow\:\mathrm{y}^{'} =? \\ $$$$\mathrm{3}.\:\mathrm{y}\:=\:\mathrm{ln}^{\mathrm{5}} \:\mathrm{sinx}\:\Rightarrow\:\mathrm{y}^{'} =? \\ $$$$\mathrm{4}.\:\mathrm{y}\:=\:\mathrm{cos}\left(\mathrm{2x}\:+\:\mathrm{3}\right)\:\Rightarrow\:\mathrm{y}^{'} =? \\ $$

Question Number 169354    Answers: 1   Comments: 0

1. ∫_0 ^1 (dx/(1 + x)) 2. ∫_0 ^( 1) (6 - x^2 )dx 3. ∫_0 ^( (π/2)) ((cosx)/(1 + sinx)) dx

$$\mathrm{1}.\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{dx}}{\mathrm{1}\:+\:\mathrm{x}} \\ $$$$\mathrm{2}.\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\left(\mathrm{6}\:-\:\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx} \\ $$$$\mathrm{3}.\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{cosx}}{\mathrm{1}\:+\:\mathrm{sinx}}\:\mathrm{dx} \\ $$

Question Number 169349    Answers: 0   Comments: 0

Question Number 169347    Answers: 4   Comments: 0

Differentiate wrt x y=sin^(−1) (2x+1) Mastermind

$${Differentiate}\:{wrt}\:{x} \\ $$$${y}={sin}^{−\mathrm{1}} \left(\mathrm{2}{x}+\mathrm{1}\right) \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169346    Answers: 0   Comments: 0

Show that substituting y=vx, x+y(dy/dx)=x(dy/dx)−y to a separable equation for v and x and its solution is log_e (x^2 +y^2 )=2tan^(−1) ((y/x)) +C Mastermind

$${Show}\:{that}\:{substituting}\:{y}={vx}, \\ $$$${x}+{y}\frac{{dy}}{{dx}}={x}\frac{{dy}}{{dx}}−{y}\:{to}\:{a}\:{separable} \\ $$$${equation}\:{for}\:{v}\:{and}\:{x}\:{and}\:{its}\: \\ $$$${solution}\:{is}\:{log}_{{e}} \left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)=\mathrm{2}{tan}^{−\mathrm{1}} \left(\frac{{y}}{{x}}\right) \\ $$$$+{C} \\ $$$$ \\ $$$${Mastermind} \\ $$$$\: \\ $$

Question Number 169342    Answers: 1   Comments: 0

Obtain the differential equation associated with the primitive y = Ae^(2x) +Be^x +C Mastermind

$${Obtain}\:{the}\:{differential}\:{equation} \\ $$$${associated}\:{with}\:{the}\:{primitive} \\ $$$${y}\:=\:{Ae}^{\mathrm{2}{x}} +{Be}^{{x}} +{C} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169340    Answers: 0   Comments: 0

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