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Question Number 169537 Answers: 0 Comments: 2

Question Number 169533 Answers: 0 Comments: 1

{ ((x+(1/y)=1)),(((1/x)+y=2)) :}⇒x^(2022) +(1/y^(2022) ) =?

$$\:\:\begin{cases}{{x}+\frac{\mathrm{1}}{{y}}=\mathrm{1}}\\{\frac{\mathrm{1}}{{x}}+{y}=\mathrm{2}}\end{cases}\Rightarrow{x}^{\mathrm{2022}} +\frac{\mathrm{1}}{{y}^{\mathrm{2022}} }\:=? \\ $$

Question Number 169527 Answers: 1 Comments: 1

evaluate the limit(if it exists) lim_(n→∞) [(((√(n^4 −2n^3 ))−n^2 )/(n+2))]^3

$$\boldsymbol{{evaluate}}\:\boldsymbol{{the}}\:\boldsymbol{{limit}}\left(\boldsymbol{{if}}\:\boldsymbol{{it}}\:\boldsymbol{{exists}}\right) \\ $$$$\boldsymbol{{lim}}_{\boldsymbol{{n}}\rightarrow\infty} \left[\frac{\sqrt{\boldsymbol{{n}}^{\mathrm{4}} −\mathrm{2}\boldsymbol{{n}}^{\mathrm{3}} }−\boldsymbol{{n}}^{\mathrm{2}} }{\boldsymbol{{n}}+\mathrm{2}}\right]^{\mathrm{3}} \\ $$

Question Number 169526 Answers: 1 Comments: 0

solve the D.E. y^′ =tan(x+y)−1

$${solve}\:{the}\:{D}.{E}. \\ $$$${y}^{'} ={tan}\left({x}+{y}\right)−\mathrm{1} \\ $$

Question Number 169508 Answers: 1 Comments: 0

Evaluate if the limit exist lim_(n→∞) (((3^n +(−2)^(n+1) )/(3^(n−2) −2^(2n−1) )))

$${Evaluate}\:{if}\:{the}\:{limit}\:{exist} \\ $$$${lim}_{\boldsymbol{{n}}\rightarrow\infty} \left(\frac{\mathrm{3}^{\boldsymbol{{n}}} +\left(−\mathrm{2}\right)^{\boldsymbol{{n}}+\mathrm{1}} }{\mathrm{3}^{\boldsymbol{{n}}−\mathrm{2}} −\mathrm{2}^{\mathrm{2}\boldsymbol{{n}}−\mathrm{1}} }\right) \\ $$

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

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