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Question Number 195708 Answers: 2 Comments: 0

Prove that : log_(((√a) − b)) ((√a) +b) = −1

$$\boldsymbol{{Prove}}\:\boldsymbol{{that}}\::\:\boldsymbol{{log}}_{\left(\sqrt{\boldsymbol{{a}}}\:−\:\boldsymbol{{b}}\right)} \left(\sqrt{\boldsymbol{{a}}}\:+\boldsymbol{{b}}\right)\:=\:−\mathrm{1} \\ $$

Question Number 195707 Answers: 1 Comments: 0

Question Number 195619 Answers: 2 Comments: 0

lim_(x→0) (( ((1+ ))^(1/3) )/ )

$$\:\: \\ $$$$ \underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{ \sqrt[{\mathrm{3}}]{\mathrm{1}+ }\: }{ } \\ $$

Question Number 195618 Answers: 4 Comments: 0

lim_(x→0) (( 2(√(1+x)) )/ )

$$\:\:\: \\ $$$$ \underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{ \mathrm{2}\sqrt{\mathrm{1}+\mathrm{x}}\: }{ } \\ $$

Question Number 195612 Answers: 1 Comments: 0

Question Number 195611 Answers: 1 Comments: 0

Question Number 195608 Answers: 1 Comments: 0

solve : ∫_0 ^( π) (sin x)^(cos x) dx

$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:{solve}\::\:\:\:\int_{\mathrm{0}} ^{\:\pi} \:\left(\mathrm{sin}\:{x}\right)^{\mathrm{cos}\:{x}} \:{dx} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 195606 Answers: 0 Comments: 1

Question Number 195602 Answers: 1 Comments: 0

solve ∫ (dx/(sin^(10) (x)+cos^(10) (x)))

$${solve}\:\int\:\frac{{dx}}{{sin}^{\mathrm{10}} \left({x}\right)+{cos}^{\mathrm{10}} \left({x}\right)} \\ $$

Question Number 195597 Answers: 0 Comments: 0

Question Number 195578 Answers: 2 Comments: 0

Question Number 195571 Answers: 2 Comments: 0

let f(x+y)+f(x−y)=2f(x)f(y)∧f((1/2))=−1 compute Σ_(k=1) ^(20) [(1/(sin (k)sin (k+f(k))))]

$${let}\:{f}\left({x}+{y}\right)+{f}\left({x}−{y}\right)=\mathrm{2}{f}\left({x}\right){f}\left({y}\right)\wedge{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=−\mathrm{1} \\ $$$${compute}\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{20}} {\sum}}\left[\frac{\mathrm{1}}{\mathrm{sin}\:\left({k}\right)\mathrm{sin}\:\left({k}+{f}\left({k}\right)\right)}\right] \\ $$

Question Number 195570 Answers: 1 Comments: 2

Given three Real numbers (x,y,z),such that x^2 +y^2 +z^2 =1 maximize x^4 +y^4 −2z^4 −3(√2)xyz

$$\mathrm{Given}\:\mathrm{three}\:\mathrm{Real}\:\mathrm{numbers}\:\left({x},{y},{z}\right),{such}\:{that} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{1} \\ $$$${maximize} \\ $$$${x}^{\mathrm{4}} +{y}^{\mathrm{4}} −\mathrm{2}{z}^{\mathrm{4}} −\mathrm{3}\sqrt{\mathrm{2}}{xyz} \\ $$

Question Number 195569 Answers: 0 Comments: 0

a_i ,b_i ,x_i be reals for i=1,2,3,...,n, such that Σ_(i=1) ^n [a_i x_i ]=0. Prove that (Σ_(i=1) ^n [x_i ^2 ])(Σ_(i=1) ^n [a_i ^2 ]Σ_(i=1) ^n [b_i ^2 ]−(Σ_(i=1) ^n [a_i b_i ])^2 )≥(Σ_(i=1) ^n [a_i ^2 ])(Σ_(i=1) ^n [b_i x_i ])^2

$${a}_{{i}} ,{b}_{{i}} ,{x}_{{i}} {be}\:{reals}\:{for}\:{i}=\mathrm{1},\mathrm{2},\mathrm{3},...,{n},\:{such}\:{that} \\ $$$$\sum_{{i}=\mathrm{1}} ^{{n}} \left[{a}_{{i}} {x}_{{i}} \right]=\mathrm{0}.\:{Prove}\:{that} \\ $$$$\left(\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left[{x}_{{i}} ^{\mathrm{2}} \right]\right)\left(\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left[{a}_{{i}} ^{\mathrm{2}} \right]\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left[{b}_{{i}} ^{\mathrm{2}} \right]−\left(\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left[{a}_{{i}} {b}_{{i}} \right]\right)^{\mathrm{2}} \right)\geqslant\left(\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left[{a}_{{i}} ^{\mathrm{2}} \right]\right)\left(\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left[{b}_{{i}} {x}_{{i}} \right]\right)^{\mathrm{2}} \\ $$

Question Number 195592 Answers: 0 Comments: 2

f(x)=((1376)/((x−1)^(ln((2/(4689)))) )) dom f(x)=? answer this

$${f}\left({x}\right)=\frac{\mathrm{1376}}{\left({x}−\mathrm{1}\right)^{{ln}\left(\frac{\mathrm{2}}{\mathrm{4689}}\right)} } \\ $$$${dom}\:{f}\left({x}\right)=? \\ $$$${answer}\:{this} \\ $$

Question Number 195590 Answers: 1 Comments: 0

Question Number 195564 Answers: 0 Comments: 0

Question Number 195560 Answers: 1 Comments: 1

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Question Number 195557 Answers: 1 Comments: 0

Question Number 195540 Answers: 1 Comments: 2

Question Number 195538 Answers: 1 Comments: 7

Number of distributions of n different articles to r different boxes so as 1)empty box allowed 2)empty box not allowed with proof...kindly help me

$${Number}\:{of}\:{distributions}\:{of} \\ $$$${n}\:{different}\:{articles}\:{to}\:{r}\:{different}\:\:{boxes} \\ $$$$\left.{so}\:{as}\:\mathrm{1}\right){empty}\:{box}\:{allowed} \\ $$$$\left.\mathrm{2}\right){empty}\:{box}\:{not}\:{allowed} \\ $$$${with}\:{proof}...{kindly}\:{help}\:{me} \\ $$

Question Number 195535 Answers: 1 Comments: 0

Question Number 199608 Answers: 2 Comments: 0

1) 3<∣2x−1∣<7 find Σx ;x∈Z 2) 4≤∣x−2∣<5 find Σx ;x∈Z

$$\left.\mathrm{1}\right)\:\:\:\mathrm{3}<\mid\mathrm{2}{x}−\mathrm{1}\mid<\mathrm{7}\:\:{find}\:\Sigma{x}\:\:\:\:;{x}\in{Z} \\ $$$$\left.\mathrm{2}\right)\:\:\:\mathrm{4}\leqslant\mid{x}−\mathrm{2}\mid<\mathrm{5}\:\:{find}\:\Sigma{x}\:\:\:\:;{x}\in{Z} \\ $$$$ \\ $$

Question Number 195532 Answers: 0 Comments: 1

2^x −2^(−x) =5 find 4^x +4^(−x) =? so soon solve it i need i have rxame tomarrow

$$\mathrm{2}^{\boldsymbol{\mathrm{x}}} −\mathrm{2}^{−\boldsymbol{\mathrm{x}}} =\mathrm{5}\:\boldsymbol{\mathrm{find}}\:\mathrm{4}^{\boldsymbol{\mathrm{x}}} +\mathrm{4}^{−\boldsymbol{\mathrm{x}}} =? \\ $$$$\boldsymbol{\mathrm{so}}\:\boldsymbol{\mathrm{soon}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{it}}\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{need}}\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{have}}\:\boldsymbol{\mathrm{rxame}}\:\boldsymbol{\mathrm{tomarrow}} \\ $$

Question Number 195521 Answers: 2 Comments: 0

2^a =50 find 2^(2a−2) =? soon as soon solve this i need so

$$\mathrm{2}^{\boldsymbol{\mathrm{a}}} =\mathrm{50}\:\:\:\:\boldsymbol{\mathrm{find}}\:\mathrm{2}^{\mathrm{2}\boldsymbol{\mathrm{a}}−\mathrm{2}} =? \\ $$$$\boldsymbol{\mathrm{soon}}\:\boldsymbol{\mathrm{as}}\:\boldsymbol{\mathrm{soon}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{need}}\:\boldsymbol{\mathrm{so}} \\ $$

Question Number 195520 Answers: 3 Comments: 0

find domine and range of function f(x,y) = (√((x+y^2 )/(x^2 +y^2 −4)))

$$\: \\ $$$$\:\:\:\:\:{find}\:{domine}\:{and}\:{range}\:{of}\:{function}\: \\ $$$$\:\:\:\:\:{f}\left({x},{y}\right)\:=\:\sqrt{\frac{{x}+{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{4}}} \\ $$$$ \\ $$$$ \\ $$

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