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Question Number 221397    Answers: 0   Comments: 1

Question Number 221393    Answers: 0   Comments: 0

a, b, c are complex number and ∣a∣ = ∣b∣=∣c∣= 1 and (a^2 /(bc))+(b^2 /(ac)) +(c^2 /(ab)) = −1 where ∣.∣ is modules function then ∣a+b+c∣ can be (A) 0 (B) 1 (C) (3/2) (D) 2

$$\:\:\:\:\:{a},\:{b},\:{c}\:{are}\:{complex}\:{number}\:{and}\: \\ $$$$\:\:\:\mid{a}\mid\:=\:\mid{b}\mid=\mid{c}\mid=\:\mathrm{1}\:{and}\:\:\frac{{a}^{\mathrm{2}} }{{bc}}+\frac{{b}^{\mathrm{2}} }{{ac}}\:+\frac{{c}^{\mathrm{2}} }{{ab}}\:=\:−\mathrm{1} \\ $$$$\:\:\:\:{where}\:\mid.\mid\:{is}\:\:{modules}\:{function} \\ $$$${then}\:\mid{a}+{b}+{c}\mid\:{can}\:{be}\: \\ $$$$\left({A}\right)\:\mathrm{0}\:\:\:\:\:\:\:\left({B}\right)\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\left({C}\right)\:\frac{\mathrm{3}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\left({D}\right)\:\mathrm{2} \\ $$

Question Number 221392    Answers: 1   Comments: 0

lim_(x→3) (√(x−3))=? 1) 0 2) 3 3) Does not exist 4) Undefined

$$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\sqrt{{x}−\mathrm{3}}=? \\ $$$$\left.\mathrm{1}\right)\:\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{3} \\ $$$$\left.\mathrm{3}\right)\:{Does}\:{not}\:{exist} \\ $$$$\left.\mathrm{4}\right)\:{Undefined} \\ $$

Question Number 221391    Answers: 0   Comments: 0

∫_0 ^( ∞) J_ν ^((1)) (t)Y_ν (t)sin(t)dt−∫_0 ^( ∞) J_ν (t)Y_ν ^((1)) (t)sin(t)dt=?? J_ν (t) is ν th Bessel function first Kind Y_ν (t) is ν th Bessel function second Kind sin(t) is sine function

$$\int_{\mathrm{0}} ^{\:\infty} {J}_{\nu} ^{\left(\mathrm{1}\right)} \left({t}\right){Y}_{\nu} \left({t}\right)\mathrm{sin}\left({t}\right)\mathrm{d}{t}−\int_{\mathrm{0}} ^{\:\infty} {J}_{\nu} \left({t}\right){Y}_{\nu} ^{\left(\mathrm{1}\right)} \left({t}\right)\mathrm{sin}\left({t}\right)\mathrm{d}{t}=?? \\ $$$${J}_{\nu} \left({t}\right)\:\mathrm{is}\:\nu\:\mathrm{th}\:\mathrm{Bessel}\:\mathrm{function}\:\mathrm{first}\:\mathrm{Kind} \\ $$$${Y}_{\nu} \left({t}\right)\:\mathrm{is}\:\nu\:\mathrm{th}\:\mathrm{Bessel}\:\mathrm{function}\:\mathrm{second}\:\mathrm{Kind} \\ $$$$\mathrm{sin}\left({t}\right)\:\mathrm{is}\:\mathrm{sine}\:\mathrm{function} \\ $$

Question Number 221388    Answers: 0   Comments: 0

Question Number 221387    Answers: 1   Comments: 0

Σ_(k = 1) ^∞ (2Σ_(n = 1) ^∞ (1/(n^2 + kn)))^2 = ?

$$ \\ $$$$\:\:\:\:\:\:\:\underset{{k}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\left(\mathrm{2}\underset{{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:+\:{kn}}\right)^{\mathrm{2}} \:=\:? \\ $$$$ \\ $$

Question Number 221382    Answers: 0   Comments: 1

Σ_(k=0) ^n ((n),(k) )^(−1)

$$\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}^{−\mathrm{1}} \\ $$

Question Number 221380    Answers: 1   Comments: 0

Problem 3.11 Find the momentum space wave function 𝚿(p,t) for a particle in the ground state of the harmoic oscillator. What is the probability (to two signficant digits)that a measurement of on a particle in this state would yield value outside the classical range(for the samenergy) Hint Look in a math table under Normal Distribution Error Function for the numerical partor use Mathematica

$$ \\ $$$$\mathrm{Problem}\:\mathrm{3}.\mathrm{11}\:\mathrm{Find}\:\mathrm{the}\:\mathrm{momentum}\:\mathrm{space}\:\mathrm{wave}\: \\ $$$$\mathrm{function}\:\boldsymbol{\Psi}\left({p},{t}\right)\:\mathrm{for}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{state}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{harmoic}\:\mathrm{oscillator}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability} \\ $$$$\left(\mathrm{to}\:\mathrm{two}\:\mathrm{signficant}\:\mathrm{digits}\right)\mathrm{that}\:\mathrm{a}\:\mathrm{measurement}\:\mathrm{of}\:\mathrm{on}\:\mathrm{a}\:\mathrm{particle}\: \\ $$$$\mathrm{in}\:\mathrm{this}\:\mathrm{state}\:\mathrm{would}\:\mathrm{yield}\:\mathrm{value}\:\mathrm{outside}\:\mathrm{the}\: \\ $$$$\mathrm{classical}\:\mathrm{range}\left(\mathrm{for}\:\mathrm{the}\:\mathrm{samenergy}\right) \\ $$$$\mathrm{Hint}\:\mathrm{Look}\:\mathrm{in}\:\mathrm{a}\:\mathrm{math}\:\mathrm{table}\:\mathrm{under}\:\mathrm{Normal}\:\mathrm{Distribution} \\ $$$$\mathrm{Error}\:\mathrm{Function}\:\mathrm{for}\:\mathrm{the}\:\mathrm{numerical}\:\mathrm{partor}\:\mathrm{use}\:\mathrm{Mathematica} \\ $$

Question Number 221377    Answers: 2   Comments: 0

Find: Ω =lim_(n→∞) (2 ((10))^(1/n) − 1)^n = ?

$$\mathrm{Find}:\:\:\:\Omega\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{2}\:\sqrt[{\boldsymbol{\mathrm{n}}}]{\mathrm{10}}\:−\:\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} \:=\:? \\ $$

Question Number 221373    Answers: 0   Comments: 1

Question Number 221370    Answers: 0   Comments: 0

Question Number 221369    Answers: 1   Comments: 2

Question Number 221368    Answers: 0   Comments: 0

why no geometry or algebra questions??

$${why}\:{no}\:{geometry}\:{or}\:{algebra}\:{questions}?? \\ $$

Question Number 221367    Answers: 1   Comments: 0

∫_0 ^( 2π) (1/(5−4sin(θ))) dθ=?? (Complex integral method)

$$\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \:\:\frac{\mathrm{1}}{\mathrm{5}−\mathrm{4sin}\left(\theta\right)}\:\mathrm{d}\theta=?? \\ $$$$\left(\mathrm{Complex}\:\mathrm{integral}\:\mathrm{method}\right) \\ $$

Question Number 221360    Answers: 1   Comments: 0

∫_0 ^( π/2) cos^(−1) (((cos x)/(1 + 2 cos x))) dx

$$ \\ $$$$\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \:\mathrm{cos}^{−\mathrm{1}} \:\left(\frac{\mathrm{cos}\:{x}}{\mathrm{1}\:+\:\mathrm{2}\:\mathrm{cos}\:{x}}\right)\:\mathrm{d}{x} \\ $$$$ \\ $$

Question Number 221359    Answers: 2   Comments: 0

Question Number 221375    Answers: 0   Comments: 0

Question Number 221354    Answers: 0   Comments: 1

Let a,b,c be there real numbers, Prove that if; sin a + sin b + sin c ≥ 2 ⇒ cos a + cos b + cos c ≤ (√5) and, sin a + sin b + sin c ≥ (3/2) ⇒ cos(a−π/6) + cos(b−π/6) + cos(c−π/6) ≥ 0 .

$$ \\ $$$$\:\:\mathrm{Let}\:{a},{b},{c}\:\mathrm{be}\:\mathrm{there}\:\mathrm{real}\:\mathrm{numbers}, \\ $$$$\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}; \\ $$$$\:\mathrm{sin}\:{a}\:+\:\mathrm{sin}\:{b}\:+\:\mathrm{sin}\:{c}\:\geqslant\:\mathrm{2}\:\:\Rightarrow\:\mathrm{cos}\:{a}\:+\:\mathrm{cos}\:{b}\:+\:\mathrm{cos}\:{c}\:\leqslant\:\sqrt{\mathrm{5}}\:\:\:\:\:\:\:\:\:\: \\ $$$$\mathrm{and}, \\ $$$$\:\mathrm{sin}\:{a}\:+\:\mathrm{sin}\:{b}\:+\:\mathrm{sin}\:{c}\:\geqslant\:\frac{\mathrm{3}}{\mathrm{2}}\:\Rightarrow\:\mathrm{cos}\left({a}−\pi/\mathrm{6}\right)\:+\:\mathrm{cos}\left({b}−\pi/\mathrm{6}\right)\:+\:\mathrm{cos}\left({c}−\pi/\mathrm{6}\right)\:\geqslant\:\mathrm{0}\:.\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 221352    Answers: 0   Comments: 0

Given real numbers a,b,c > 0 , such that a + b + c = a^3 + b^3 + c^3 , Prove ; (a^3 /(a^4 + b + c)) + (b^3 /(b^4 + c + a)) + (c^3 /(c^4 + a + b)) ≤ 1

$$ \\ $$$$\:\:\:\:\mathrm{Given}\:\mathrm{real}\:\mathrm{numbers}\:{a},{b},{c}\:>\:\mathrm{0}\:, \\ $$$$\:\:\mathrm{such}\:\mathrm{that}\:{a}\:+\:{b}\:+\:{c}\:=\:{a}^{\mathrm{3}} \:+\:{b}^{\mathrm{3}} \:+\:{c}^{\mathrm{3}} \:, \\ $$$$\:\mathrm{Prove}\:;\:\frac{{a}^{\mathrm{3}} }{{a}^{\mathrm{4}} \:+\:{b}\:+\:{c}}\:+\:\frac{{b}^{\mathrm{3}} }{{b}^{\mathrm{4}} \:+\:{c}\:+\:{a}}\:+\:\frac{{c}^{\mathrm{3}} }{{c}^{\mathrm{4}} \:+\:\:{a}\:+\:{b}}\:\leqslant\:\mathrm{1} \\ $$$$\: \\ $$

Question Number 221350    Answers: 1   Comments: 1

∫_0 ^∞ ((cos πx)/(Γ(2+x)Γ(2−x)))dx

$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{cos}\:\pi{x}}{\Gamma\left(\mathrm{2}+{x}\right)\Gamma\left(\mathrm{2}−{x}\right)}{dx} \\ $$$$ \\ $$$$ \\ $$

Question Number 221348    Answers: 2   Comments: 0

lim_(x→2) ((4−2^x )/(x−2))

$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{4}−\mathrm{2}^{{x}} }{{x}−\mathrm{2}} \\ $$

Question Number 221347    Answers: 1   Comments: 0

lim_(x→2) ((4−x^2 )/(x−2))

$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{4}−{x}^{\mathrm{2}} }{{x}−\mathrm{2}} \\ $$

Question Number 221342    Answers: 0   Comments: 0

Question Number 221332    Answers: 1   Comments: 0

Question Number 221315    Answers: 0   Comments: 1

if function z is analytic within and on a simple closed curve C,−and z_0 is a point within C using cauchy′s integral formula ∮((sin𝛑z^2 +cos𝛑z^2 )/((x−1)(x−2)))dz

$$\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{function}}\:\boldsymbol{\mathrm{z}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{analytic}}\:\boldsymbol{\mathrm{within}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{simple}} \\ $$$$\boldsymbol{\mathrm{closed}}\:\boldsymbol{\mathrm{curve}}\:\boldsymbol{\mathrm{C}},−\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{z}}_{\mathrm{0}} \:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{point}}\:\boldsymbol{\mathrm{within}}\:\boldsymbol{\mathrm{C}} \\ $$$$\boldsymbol{\mathrm{using}}\:\boldsymbol{\mathrm{cauchy}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{integral}}\:\boldsymbol{\mathrm{formula}} \\ $$$$\oint\frac{\boldsymbol{\mathrm{sin}\pi\mathrm{z}}^{\mathrm{2}} +\boldsymbol{\mathrm{cos}\pi\mathrm{z}}^{\mathrm{2}} }{\left(\boldsymbol{\mathrm{x}}−\mathrm{1}\right)\left(\boldsymbol{\mathrm{x}}−\mathrm{2}\right)}\boldsymbol{\mathrm{dz}} \\ $$

Question Number 221322    Answers: 3   Comments: 0

Solve for x x^(1/a) +(√x^((1/a)+(1/b)) )=x^(1/b)

$$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$${x}^{\frac{\mathrm{1}}{{a}}} +\sqrt{{x}^{\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}} }={x}^{\frac{\mathrm{1}}{{b}}} \\ $$

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