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Question Number 55129 Answers: 1 Comments: 1

question 54995 reposted ∫((x^3 +x^2 ))^(1/3) dx=?

$$\mathrm{question}\:\mathrm{54995}\:\mathrm{reposted} \\ $$$$\int\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +{x}^{\mathrm{2}} }{dx}=? \\ $$

Question Number 55126 Answers: 0 Comments: 0

Question Number 55119 Answers: 1 Comments: 1

How many numbers, divisible by 5, can be made with the digits 2,3,4 and 5 where no digit is being used more than once in each number?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers},\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{5},\:\mathrm{can} \\ $$$$\mathrm{be}\:\mathrm{made}\:\mathrm{with}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{2},\mathrm{3},\mathrm{4}\:\mathrm{and}\:\mathrm{5}\:\mathrm{where} \\ $$$$\mathrm{no}\:\mathrm{digit}\:\mathrm{is}\:\mathrm{being}\:\mathrm{used}\:\mathrm{more}\:\mathrm{than}\:\mathrm{once} \\ $$$$\mathrm{in}\:\mathrm{each}\:\mathrm{number}? \\ $$

Question Number 55115 Answers: 0 Comments: 4

Question Number 55108 Answers: 0 Comments: 0

Question Number 55104 Answers: 0 Comments: 3

Question Number 55100 Answers: 1 Comments: 5

Question Number 55099 Answers: 1 Comments: 0

Show that for n ∈ N, Σ_(r=0) ^n P_r ^n = ⌊n! e⌋ where ⌊x⌋ denotes the greatest integer ≤ x and P_r ^n = ((n!)/((n − r)!))

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{for}\:{n}\:\in\:\mathbb{N}, \\ $$$$\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:{P}_{{r}} ^{{n}} \:=\:\lfloor{n}!\:{e}\rfloor \\ $$$$\mathrm{where}\:\lfloor{x}\rfloor\:\mathrm{denotes}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\:\leqslant\:{x} \\ $$$$\mathrm{and}\:{P}_{{r}} ^{{n}} \:=\:\frac{{n}!}{\left({n}\:−\:{r}\right)!} \\ $$

Question Number 55089 Answers: 0 Comments: 1

∫_( 0) ^1 (1/((x^2 +1)^(3/2) )) dx =

$$\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}} }\:{dx}\:= \\ $$

Question Number 55088 Answers: 0 Comments: 0

Question Number 55087 Answers: 0 Comments: 1

Please any web site or ebook to learn LATEX ? Thank you.

$$\mathrm{Please}\:\mathrm{any}\:\mathrm{web}\:\mathrm{site}\:\mathrm{or}\:\mathrm{ebook}\:\mathrm{to}\:\mathrm{learn} \\ $$$${LATEX}\:? \\ $$$$\mathrm{Thank}\:\mathrm{you}. \\ $$

Question Number 55094 Answers: 2 Comments: 2

(((1/4) + (1/(16)) + (1/(36)) + (1/(64)) + ...)/(1 + (1/9) + (1/(25)) + (1/(49)) + ...)) = x 3x^2 + 2x − 1 = ?

$$\frac{\frac{\mathrm{1}}{\mathrm{4}}\:+\:\frac{\mathrm{1}}{\mathrm{16}}\:+\:\frac{\mathrm{1}}{\mathrm{36}}\:+\:\frac{\mathrm{1}}{\mathrm{64}}\:+\:...}{\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{9}}\:+\:\frac{\mathrm{1}}{\mathrm{25}}\:+\:\frac{\mathrm{1}}{\mathrm{49}}\:+\:...}\:\:=\:\:{x} \\ $$$$\mathrm{3}{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:−\:\mathrm{1}\:\:=\:\:? \\ $$

Question Number 55083 Answers: 0 Comments: 0

Question Number 55076 Answers: 1 Comments: 0

Known polynom P(z)=a_0 z^n +a_1 z^(n−1) +…+a_(n ) With explain real number. If z_0 =3−4i form root is from polynom, then one other root defonitely appeared is..

$$\mathrm{Known}\:\mathrm{polynom} \\ $$$$\mathrm{P}\left({z}\right)={a}_{\mathrm{0}} {z}^{{n}} +{a}_{\mathrm{1}} {z}^{{n}−\mathrm{1}} +\ldots+{a}_{{n}\:} \mathrm{With} \\ $$$$\mathrm{explain}\:\mathrm{real}\:\mathrm{number}.\:\mathrm{If}\:{z}_{\mathrm{0}} =\mathrm{3}−\mathrm{4}{i} \\ $$$$\mathrm{form}\:\mathrm{root}\:\mathrm{is}\:\mathrm{from}\:\mathrm{polynom}, \\ $$$$\mathrm{then}\:\mathrm{one}\:\mathrm{other}\:\mathrm{root}\:\mathrm{defonitely}\:\mathrm{appeared} \\ $$$$\mathrm{is}.. \\ $$

Question Number 55070 Answers: 0 Comments: 1

Factorised the polynom z^4 +1 be polynom with lower degree, but have real coefficient

$$\mathrm{Factorised}\:\mathrm{the}\:\mathrm{polynom}\:{z}^{\mathrm{4}} +\mathrm{1}\: \\ $$$$\mathrm{be}\:\mathrm{polynom}\:\mathrm{with}\:\mathrm{lower}\:\mathrm{degree}, \\ $$$$\mathrm{but}\:\mathrm{have}\:\mathrm{real}\:\mathrm{coefficient} \\ $$

Question Number 55069 Answers: 1 Comments: 3

Known analytic function f(z)=((2(z−2))/(z(z−4))) and written as f(z)=Σ_(n=0) ^(∝) a_n (z−1)^n The value of a_(100) is...

$$\mathrm{Known}\:\mathrm{analytic}\:\mathrm{function} \\ $$$${f}\left({z}\right)=\frac{\mathrm{2}\left({z}−\mathrm{2}\right)}{{z}\left({z}−\mathrm{4}\right)} \\ $$$$\mathrm{and}\:\mathrm{written}\:\mathrm{as}\:{f}\left({z}\right)=\underset{{n}=\mathrm{0}} {\overset{\propto} {\Sigma}}\:{a}_{{n}} \left({z}−\mathrm{1}\right)^{{n}} \\ $$$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:{a}_{\mathrm{100}} \:\mathrm{is}... \\ $$

Question Number 55068 Answers: 0 Comments: 0

Calculate value of ∫_C e^(2/z) dz if C is unit circle

$$\mathrm{Calculate}\:\mathrm{value}\:\mathrm{of}\:\int_{{C}} {e}^{\frac{\mathrm{2}}{{z}}} \:{dz} \\ $$$$\mathrm{if}\:{C}\:\mathrm{is}\:\mathrm{unit}\:\mathrm{circle} \\ $$$$ \\ $$

Question Number 55067 Answers: 0 Comments: 0

Known C circle centered at 0. Find value than ∫_C (dz/(1−z))

$$\mathrm{Known}\:\:{C}\:\mathrm{circle}\:\mathrm{centered}\:\mathrm{at}\:\mathrm{0}. \\ $$$$\mathrm{Find}\:\mathrm{value}\:\mathrm{than}\:\int_{{C}} \frac{{dz}}{\mathrm{1}−{z}} \\ $$

Question Number 55066 Answers: 0 Comments: 0

Find radius convergence for series 1−z^2 +z^4 −z^6 +...

$$\mathrm{Find}\:\mathrm{radius}\:\mathrm{convergence}\:\mathrm{for}\:\mathrm{series} \\ $$$$\mathrm{1}−{z}^{\mathrm{2}} +{z}^{\mathrm{4}} −{z}^{\mathrm{6}} +... \\ $$

Question Number 55059 Answers: 0 Comments: 0

Find the number of root equation z^4 −5z+1=0 in 1 ≤ ∣z∣ ≤ 2

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{root}\:\mathrm{equation} \\ $$$${z}^{\mathrm{4}} −\mathrm{5}{z}+\mathrm{1}=\mathrm{0}\:\mathrm{in}\:\mathrm{1}\:\leqslant\:\mid{z}\mid\:\leqslant\:\mathrm{2} \\ $$

Question Number 55058 Answers: 0 Comments: 0

Prove that: P_n (z)=a_0 z^n +a_1 z^(n−1) +...+a_(n−1) z+a_n at least have one value of zero

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{P}_{{n}} \left({z}\right)={a}_{\mathrm{0}} {z}^{{n}} +{a}_{\mathrm{1}} {z}^{{n}−\mathrm{1}} +...+{a}_{{n}−\mathrm{1}} {z}+{a}_{{n}} \\ $$$$\mathrm{at}\:\mathrm{least}\:\mathrm{have}\:\mathrm{one}\:\:\mathrm{value}\:\mathrm{of}\:\mathrm{zero} \\ $$

Question Number 55057 Answers: 0 Comments: 0

Prove that Ln(z+1)=z−(z^2 /2)+(z^3 /3)−(z^4 /4)+... for ∣z∣< 1

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{Ln}\left({z}+\mathrm{1}\right)={z}−\frac{{z}^{\mathrm{2}} }{\mathrm{2}}+\frac{{z}^{\mathrm{3}} }{\mathrm{3}}−\frac{{z}^{\mathrm{4}} }{\mathrm{4}}+... \\ $$$$\mathrm{for}\:\mid{z}\mid<\:\mathrm{1} \\ $$

Question Number 55055 Answers: 1 Comments: 0

Question Number 55054 Answers: 0 Comments: 0

Question Number 55052 Answers: 0 Comments: 3

Question Number 55051 Answers: 0 Comments: 1

calculate lim_(n→+∞) ∫_0 ^1 (dx/(1+x+x^2 +...+x^n ))

$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dx}}{\mathrm{1}+{x}+{x}^{\mathrm{2}} \:+...+{x}^{{n}} } \\ $$

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