Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 493

Question Number 169504    Answers: 0   Comments: 1

Question Number 169501    Answers: 1   Comments: 0

Question Number 169498    Answers: 1   Comments: 3

Question Number 169497    Answers: 1   Comments: 0

Determine all functions f:R→R such that af(b)+bf(a)=(a+b)f((√(ab))) ∀ab>0

$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{functions}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{a}{f}\left(\mathrm{b}\right)+\mathrm{b}{f}\left(\mathrm{a}\right)=\left(\mathrm{a}+\mathrm{b}\right){f}\left(\sqrt{\mathrm{ab}}\right)\:\forall\mathrm{ab}>\mathrm{0} \\ $$

Question Number 169514    Answers: 1   Comments: 2

evaluate the following limit (if it exists) lim_(n→∞) ((ln^2 (n+1))/((n−1)^2 ))

$$\boldsymbol{{evaluate}}\:\boldsymbol{{the}}\:\boldsymbol{{following}}\:\boldsymbol{{limit}} \\ $$$$\left(\boldsymbol{{if}}\:\boldsymbol{{it}}\:\boldsymbol{{exists}}\right) \\ $$$$\boldsymbol{{lim}}_{\boldsymbol{{n}}\rightarrow\infty} \frac{\boldsymbol{{ln}}^{\mathrm{2}} \left(\boldsymbol{{n}}+\mathrm{1}\right)}{\left(\boldsymbol{{n}}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 169481    Answers: 0   Comments: 0

Question Number 169480    Answers: 1   Comments: 0

Question Number 169479    Answers: 2   Comments: 2

lim_(x→4) (((cos a)^x −(sin a)^x −cos 2a)/(x−4)) =?

$$\:\:\:\underset{{x}\rightarrow\mathrm{4}} {\mathrm{lim}}\:\frac{\left(\mathrm{cos}\:{a}\right)^{{x}} −\left(\mathrm{sin}\:{a}\right)^{{x}} −\mathrm{cos}\:\mathrm{2}{a}}{{x}−\mathrm{4}}\:=? \\ $$

Question Number 169466    Answers: 1   Comments: 0

Question Number 169458    Answers: 2   Comments: 1

Question Number 169448    Answers: 1   Comments: 6

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

  Pg 488      Pg 489      Pg 490      Pg 491      Pg 492      Pg 493      Pg 494      Pg 495      Pg 496      Pg 497   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com