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Question Number 178678    Answers: 0   Comments: 0

Cacul lim_(n→+∝) n[(e^(−2(√n)) /e^(−2(√(n+1))) ) −1]=....

$${Cacul} \\ $$$${li}\underset{{n}\rightarrow+\propto} {{m}}\:\:\:\:{n}\left[\frac{{e}^{−\mathrm{2}\sqrt{{n}}} }{{e}^{−\mathrm{2}\sqrt{{n}+\mathrm{1}}} }\:−\mathrm{1}\right]=.... \\ $$

Question Number 178673    Answers: 2   Comments: 0

Question Number 178657    Answers: 0   Comments: 0

calculate I=∫_0 ^( (π/4)) (( sin(x))/(1+ tan(2x))) dx = ?

$$ \\ $$$$\:\:\:\:\:\:{calculate} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{\:\:\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{1}+\:\mathrm{tan}\left(\mathrm{2x}\right)}\:\mathrm{dx}\:=\:? \\ $$$$\: \\ $$

Question Number 178653    Answers: 0   Comments: 0

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Question Number 178652    Answers: 0   Comments: 0

calculer la branche infinie de(√(x^2 +2x+4))

$${calculer}\:{la}\:{branche}\:{infinie}\:{de}\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}} \\ $$

Question Number 178686    Answers: 2   Comments: 0

Given 2x^2 y^2 +12y^2 =7x^2 +647 for x,y ε Z . Find the remaider if 3x^2 y^4 divide by 11 .

$$\:{Given}\:\mathrm{2}{x}^{\mathrm{2}} {y}^{\mathrm{2}} +\mathrm{12}{y}^{\mathrm{2}} =\mathrm{7}{x}^{\mathrm{2}} +\mathrm{647}\: \\ $$$$\:{for}\:{x},{y}\:\varepsilon\:\mathbb{Z}\:. \\ $$$$\:{Find}\:{the}\:{remaider}\:{if}\:\mathrm{3}{x}^{\mathrm{2}} {y}^{\mathrm{4}} \:{divide}\:{by} \\ $$$$\:\:\mathrm{11}\:. \\ $$

Question Number 178647    Answers: 1   Comments: 0

Question Number 178645    Answers: 0   Comments: 4

determiner la surface exterieure au carre bleu dans laquelle la chevre pourra circuler

$${determiner}\:{la}\:{surface}\:{exterieure}\:{au}\:{carre}\:{bleu}\:{dans}\:{laquelle} \\ $$$$\:{la}\:{chevre}\:{pourra}\:{circuler} \\ $$

Question Number 178640    Answers: 0   Comments: 0

∀−1≤a≤1, ∃0≤b≤2, x^2 −2ax+a≥∣b−1∣+∣b−2∣ find the range of x. (x∈R)

$$\forall−\mathrm{1}\leqslant{a}\leqslant\mathrm{1},\:\exists\mathrm{0}\leqslant{b}\leqslant\mathrm{2},\:{x}^{\mathrm{2}} −\mathrm{2}{ax}+{a}\geqslant\mid{b}−\mathrm{1}\mid+\mid{b}−\mathrm{2}\mid \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{x}.\:\left({x}\in\mathbb{R}\right) \\ $$

Question Number 178639    Answers: 0   Comments: 0

A set of five numbers has: mode 24 median 21 mean 20 what are the five numbers?

$$\mathrm{A}\:\mathrm{set}\:\mathrm{of}\:\mathrm{five}\:\mathrm{numbers}\:\mathrm{has}: \\ $$$$\mathrm{mode}\:\mathrm{24} \\ $$$$\mathrm{median}\:\mathrm{21} \\ $$$$\mathrm{mean}\:\mathrm{20} \\ $$$$\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{five}\:\mathrm{numbers}? \\ $$

Question Number 178635    Answers: 1   Comments: 2

solution set of log_x^(2 ) ((x/(∣x∣))−x)≥0

$$\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\:\mathrm{log}_{\mathrm{x}^{\mathrm{2}\:\:\:} } \left(\frac{\mathrm{x}}{\mid\mathrm{x}\mid}−\mathrm{x}\right)\geqslant\mathrm{0} \\ $$

Question Number 178632    Answers: 0   Comments: 7

show that range of the ff projection obtained by algebric expression R=(ucosθ)(usinθ)+(√((usinθ)^2 +2gh))

$${show}\:{that}\:{range}\:{of}\:{the}\:{ff}\:{projection} \\ $$$$\:{obtained}\:{by}\:{algebric}\:{expression}\: \\ $$$${R}=\left({ucos}\theta\right)\left({usin}\theta\right)+\sqrt{\left({usin}\theta\right)^{\mathrm{2}} +\mathrm{2}{gh}} \\ $$

Question Number 178628    Answers: 0   Comments: 7

Question Number 178626    Answers: 1   Comments: 3

Question Number 178624    Answers: 1   Comments: 0

let f:[0,1]→ R be given by f(x) = (((1+x^(1/3) )^3 +(1−x^(1/3) )^3 )/(8(1+x))) then max{f(x): x∈[0,1]}−min{f(x):x∈[0,1]} is

$$\:\:\:\:\:\:\:\boldsymbol{\mathrm{let}}\:\boldsymbol{\mathrm{f}}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\:\mathbb{R}\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{given}}\:\boldsymbol{\mathrm{by}} \\ $$$$\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)\:=\:\:\frac{\left(\mathrm{1}+\boldsymbol{\mathrm{x}}^{\frac{\mathrm{1}}{\mathrm{3}}} \right)^{\mathrm{3}} +\left(\mathrm{1}−\boldsymbol{\mathrm{x}}^{\frac{\mathrm{1}}{\mathrm{3}}} \right)^{\mathrm{3}} }{\mathrm{8}\left(\mathrm{1}+\boldsymbol{\mathrm{x}}\right)}\:\:\:\boldsymbol{\mathrm{then}} \\ $$$$\:\:\boldsymbol{\mathrm{max}}\left\{\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right):\:\boldsymbol{\mathrm{x}}\in\left[\mathrm{0},\mathrm{1}\right]\right\}−\boldsymbol{\mathrm{min}}\left\{\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right):\boldsymbol{\mathrm{x}}\in\left[\mathrm{0},\mathrm{1}\right]\right\} \\ $$$$\mathrm{is} \\ $$

Question Number 178612    Answers: 2   Comments: 0

Be calm then solve ∣((x^2 +7x−8)/(x+3))∣≥ 2

$${Be}\:{calm}\:{then}\:{solve}\:\mid\frac{{x}^{\mathrm{2}} +\mathrm{7}{x}−\mathrm{8}}{{x}+\mathrm{3}}\mid\geqslant\:\mathrm{2} \\ $$

Question Number 178609    Answers: 1   Comments: 0

Question Number 178600    Answers: 2   Comments: 0

Solve 1st: ∣x−9∣≤ −1 , 2nd: ∣10x+1∣> −4

$${Solve}\:\mathrm{1}{st}:\:\mid{x}−\mathrm{9}\mid\leqslant\:−\mathrm{1}\:,\:\mathrm{2}{nd}:\:\mid\mathrm{10}{x}+\mathrm{1}\mid>\:−\mathrm{4} \\ $$

Question Number 179996    Answers: 0   Comments: 0

Question Number 178596    Answers: 1   Comments: 4

Let (√a)+ (√b)= (√(2023)) , Find values of a, b ∈ N

$${Let}\:\sqrt{{a}}+\:\sqrt{{b}}=\:\sqrt{\mathrm{2023}}\:\:\:,\:{Find}\:{values}\:{of}\:{a},\:{b}\:\in\:\mathbb{N} \\ $$

Question Number 178595    Answers: 1   Comments: 0

Solve ((2x)/(x+1))≥ 3

$${Solve}\:\frac{\mathrm{2}{x}}{{x}+\mathrm{1}}\geqslant\:\mathrm{3} \\ $$

Question Number 178582    Answers: 1   Comments: 3

show that Range of the ff projection obtained by algebric expression R=(((ucosθ)(usinθ)+(√((usinθ)^2 +2gh)))/g) help me please

$${show}\:{that}\:{Range}\:{of}\:{the}\:{ff}\:{projection}\: \\ $$$${obtained}\:{by}\:{algebric}\:{expression} \\ $$$${R}=\frac{\left({ucos}\theta\right)\left({usin}\theta\right)+\sqrt{\left({usin}\theta\right)^{\mathrm{2}} +\mathrm{2}{gh}}}{{g}}\:\:\:{help}\:{me}\:{please} \\ $$

Question Number 178586    Answers: 0   Comments: 0

Question Number 178577    Answers: 1   Comments: 0

prove that (a)cosh^(−1) x=±ln (x+(√(x^2 −1))) (b)tanh^(−1) x=(1/2)ln (((x+1)/(x−1))),∣x∣<1

$$\mathrm{prove}\:\mathrm{that} \\ $$$$\left(\mathrm{a}\right)\mathrm{cosh}\:^{−\mathrm{1}} \mathrm{x}=\pm\mathrm{ln}\:\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\right) \\ $$$$\left(\mathrm{b}\right)\mathrm{tanh}\:^{−\mathrm{1}} \mathrm{x}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\left(\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}\right),\mid\mathrm{x}\mid<\mathrm{1} \\ $$

Question Number 178576    Answers: 0   Comments: 0

If a>b>0 prove that b<((ae^x +be^(−x) )/(e^x +e^(−x) ))<a

$$\mathrm{If}\:\mathrm{a}>\mathrm{b}>\mathrm{0}\:\:\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{b}<\frac{\mathrm{ae}^{\mathrm{x}} +\mathrm{be}^{−\mathrm{x}} }{\mathrm{e}^{\mathrm{x}} +\mathrm{e}^{−\mathrm{x}} }<\mathrm{a} \\ $$

Question Number 178575    Answers: 1   Comments: 0

Solve for x e^(sinh^(−1) x) =1+e^(cosh^(−1) x)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x} \\ $$$$\mathrm{e}^{\mathrm{sinh}\:^{−\mathrm{1}} \mathrm{x}} =\mathrm{1}+\mathrm{e}^{\mathrm{cosh}\:^{−\mathrm{1}} \mathrm{x}} \\ $$

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