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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

Question Number 221322 Answers: 3 Comments: 0

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

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

Question Number 221321 Answers: 0 Comments: 0

if 0<x<y<e^2 then y^(√x) +x^2 +6xy+18y^2 +(8/x)+((16)/(9x^2 y^2 ))>2+x^(√y)

$${if}\:\mathrm{0}<{x}<{y}<{e}^{\mathrm{2}} \:{then} \\ $$$${y}^{\sqrt{{x}}} +{x}^{\mathrm{2}} +\mathrm{6}{xy}+\mathrm{18}{y}^{\mathrm{2}} +\frac{\mathrm{8}}{{x}}+\frac{\mathrm{16}}{\mathrm{9}{x}^{\mathrm{2}} {y}^{\mathrm{2}} }>\mathrm{2}+{x}^{\sqrt{{y}}} \\ $$

Question Number 221306 Answers: 2 Comments: 0

Σ_(n=1) ^∞ ((csch^2 (πn))/n^2 )

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{csch}^{\mathrm{2}} \left(\pi{n}\right)}{{n}^{\mathrm{2}} } \\ $$

Question Number 221298 Answers: 5 Comments: 0

Find the area of △ABC. sides are (√(20)), (√(26)). and (√(34)) .

$${Find}\:{the}\:{area}\:{of}\:\bigtriangleup{ABC}. \\ $$$${sides}\:{are}\:\sqrt{\mathrm{20}},\:\sqrt{\mathrm{26}}.\:{and}\:\sqrt{\mathrm{34}}\:. \\ $$