Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 1180

Question Number 98884 Answers: 2 Comments: 0

calculate ∫_0 ^∞ ((lnx)/((x+1)^4 ))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{lnx}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{4}} }\mathrm{dx} \\ $$

Question Number 98883 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/(x^8 +x^4 +1))

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{8}} \:+\mathrm{x}^{\mathrm{4}} +\mathrm{1}} \\ $$

Question Number 98880 Answers: 0 Comments: 0

Given the sequence (u_n )_(n∈N^∗ ) defined by { (((1/2^n ) if n≡0mod(3))),(((1/3^n )+1 if n≡1mod(3))),((((u_(n−1) +u_(n+2) )/2) if n≡2mod(3))) :} a\Determine the first−8^(th) terms of (u_n )_(n∈N^∗ ) b\Show that the sequences (v_n )_(n∈N) , (w_n )_(n∈N) , and (z_n )_(n∈N) where v_n =u_(3n) , w_n =u_(3n+1) and z_n =u_(3n+2 ) are convervent and find their respective limits c\Deduce the nature of (u_n )_(n∈N^∗ )

$$\mathcal{G}\mathrm{iven}\:\mathrm{the}\:\mathrm{sequence}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}^{\ast} } \:\mathrm{defined}\:\mathrm{by}\:\begin{cases}{\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{n}} }\:\mathrm{if}\:\mathrm{n}\equiv\mathrm{0mod}\left(\mathrm{3}\right)}\\{\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{n}} }+\mathrm{1}\:\:\:\mathrm{if}\:\mathrm{n}\equiv\mathrm{1mod}\left(\mathrm{3}\right)}\\{\frac{\mathrm{u}_{\mathrm{n}−\mathrm{1}} +\mathrm{u}_{\mathrm{n}+\mathrm{2}} }{\mathrm{2}}\:\mathrm{if}\:\mathrm{n}\equiv\mathrm{2mod}\left(\mathrm{3}\right)}\end{cases} \\ $$$$\mathrm{a}\backslash\mathcal{D}\mathrm{etermine}\:\mathrm{the}\:\mathrm{first}−\mathrm{8}^{\mathrm{th}} \:\mathrm{terms}\:\mathrm{of}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}^{\ast} } \\ $$$$\mathrm{b}\backslash\mathcal{S}\mathrm{how}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sequences}\:\left(\mathrm{v}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} ,\:\left(\mathrm{w}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} ,\:\mathrm{and}\:\left(\mathrm{z}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} \\ $$$$\mathrm{where}\:\mathrm{v}_{\mathrm{n}} =\mathrm{u}_{\mathrm{3n}} ,\:\mathrm{w}_{\mathrm{n}} =\mathrm{u}_{\mathrm{3n}+\mathrm{1}} \:\mathrm{and}\:\mathrm{z}_{\mathrm{n}} =\mathrm{u}_{\mathrm{3n}+\mathrm{2}\:} \mathrm{are}\:\mathrm{convervent} \\ $$$$\mathrm{and}\:\mathrm{find}\:\mathrm{their}\:\mathrm{respective}\:\mathrm{limits} \\ $$$$\mathrm{c}\backslash\mathcal{D}\mathrm{educe}\:\mathrm{the}\:\mathrm{nature}\:\mathrm{of}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}^{\ast} } \\ $$

Question Number 98859 Answers: 2 Comments: 1

Question Number 98858 Answers: 3 Comments: 12

lim_(x→0) (√(x+(√(x+(√(x+(√(x.......))))))))

$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}.......}}}} \\ $$$$ \\ $$

Question Number 98857 Answers: 0 Comments: 0

Question Number 98848 Answers: 0 Comments: 0

Σ_(n=1) ^∞ Σ_(k=1) ^∞ (((−1)^(n+k+1) (1+k)^2 )/(n(n+k+1)^4 ))

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}+{k}+\mathrm{1}} \left(\mathrm{1}+{k}\right)^{\mathrm{2}} }{{n}\left({n}+{k}+\mathrm{1}\right)^{\mathrm{4}} } \\ $$

Question Number 98844 Answers: 3 Comments: 0

Please explain: Σ_(1 ≤ i < j ≤ n) ij = Σ_(j = 2) ^n ((j(j − 1)j)/2) I want to know how L.H.S = R.H.S

$$\mathrm{Please}\:\mathrm{explain}:\:\:\:\:\:\:\underset{\mathrm{1}\:\leqslant\:\boldsymbol{\mathrm{i}}\:<\:\boldsymbol{\mathrm{j}}\:\leqslant\:\boldsymbol{\mathrm{n}}} {\sum}\boldsymbol{\mathrm{ij}}\:\:\:\:=\:\:\:\underset{\boldsymbol{\mathrm{j}}\:\:=\:\:\mathrm{2}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\frac{\boldsymbol{\mathrm{j}}\left(\boldsymbol{\mathrm{j}}\:−\:\mathrm{1}\right)\boldsymbol{\mathrm{j}}}{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{I}}\:\mathrm{want}\:\mathrm{to}\:\mathrm{know}\:\mathrm{how}\:\mathrm{L}.\mathrm{H}.\mathrm{S}\:\:=\:\:\mathrm{R}.\mathrm{H}.\mathrm{S} \\ $$

Question Number 98843 Answers: 0 Comments: 1

I′ve got a question: What differences 2.083 and 2.084 versions with?

$$\boldsymbol{{I}}'\boldsymbol{{ve}}\:\boldsymbol{{got}}\:\boldsymbol{{a}}\:\boldsymbol{{question}}: \\ $$$$\boldsymbol{{What}}\:\boldsymbol{{differences}}\:\mathrm{2}.\mathrm{083}\:\boldsymbol{{and}}\:\mathrm{2}.\mathrm{084}\:\boldsymbol{{versions}}\:\boldsymbol{{with}}? \\ $$

Question Number 98842 Answers: 2 Comments: 1

let f(x) be a dolvnomial of degree 4 such that f(1)=1 , f(2)=2 ,f(3)=3,f(4)=4 then f(6)=?

$${let}\:{f}\left({x}\right)\:{be}\:{a}\:{dolvnomial}\:{of}\:{degree}\:\mathrm{4}\: \\ $$$${such}\:{that}\:{f}\left(\mathrm{1}\right)=\mathrm{1}\:,\:{f}\left(\mathrm{2}\right)=\mathrm{2}\:,{f}\left(\mathrm{3}\right)=\mathrm{3},{f}\left(\mathrm{4}\right)=\mathrm{4} \\ $$$${then}\:{f}\left(\mathrm{6}\right)=? \\ $$

Question Number 98833 Answers: 1 Comments: 1

Question Number 98831 Answers: 1 Comments: 1

Question Number 98826 Answers: 0 Comments: 2

Given ∫_0 ^∞ (dx/(a^2 +x^2 )) = (π/(2a)) find ∫_0 ^∞ (dx/((a^2 +x^2 )^3 )) ?

$${Given}\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{dx}}{{a}^{\mathrm{2}} +{x}^{\mathrm{2}} }\:=\:\frac{\pi}{\mathrm{2}{a}} \\ $$$${find}\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{dx}}{\left({a}^{\mathrm{2}} +{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:? \\ $$

Question Number 98823 Answers: 0 Comments: 2

Question Number 98821 Answers: 1 Comments: 0

∫ _0 ^∞ (dx/(a^2 +x^2 )) = ?

$$\int\overset{\infty} {\:}_{\mathrm{0}} \frac{{dx}}{{a}^{\mathrm{2}} +{x}^{\mathrm{2}} }\:=\:? \\ $$

Question Number 98818 Answers: 0 Comments: 0

Question Number 98816 Answers: 0 Comments: 0

prove that (V^( μ) )_(;μ) =((((√(−g))V^( μ) )_(;μ) )/(√(−g)))

$${prove}\:{that} \\ $$$$ \\ $$$$\left({V}^{\:\mu} \right)_{;\mu} =\frac{\left(\sqrt{−{g}}{V}^{\:\mu} \right)_{;\mu} }{\sqrt{−{g}}} \\ $$

Question Number 98815 Answers: 1 Comments: 0

what is heisenberg uncertainty principle?

$${what}\:{is}\:{heisenberg}\:{uncertainty}\:{principle}? \\ $$$$ \\ $$

Question Number 98808 Answers: 1 Comments: 0

Question Number 98806 Answers: 0 Comments: 1

for a is integer number such that ∣∣x−1∣ −2∣ ≤ a exactly has 2013 solution

$$\mathrm{for}\:{a}\:\mathrm{is}\:\mathrm{integer}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mid\mid{x}−\mathrm{1}\mid\:−\mathrm{2}\mid\:\leqslant\:{a}\:\:\mathrm{exactly}\:\mathrm{has}\:\mathrm{2013} \\ $$$$\mathrm{solution} \\ $$

Question Number 98788 Answers: 2 Comments: 0

lim_(n→∞) (1/n)[ (n+1)(n+2)...(n+n)_ ^ ]^(1/n)

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{n}}\left[\:\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{2}\right)...\left(\mathrm{n}+\mathrm{n}\right)_{} ^{} \right]^{\frac{\mathrm{1}}{\mathrm{n}}} \\ $$

Question Number 98776 Answers: 0 Comments: 0

∫_0 ^∞ (((x−1))/(ln(F(x)(√5)+cos(πx)(ϕ)^(−x) −1)(√(F(x)(√5)+cos(πx)(ϕ)^(−x) −1))))dx F(x)=Fib(x)=xth Extended fibonacci number f:R→R ϕ=((1+(√5))/2)

$$\int_{\mathrm{0}} ^{\infty} \frac{\left({x}−\mathrm{1}\right)}{{ln}\left({F}\left({x}\right)\sqrt{\mathrm{5}}+{cos}\left(\pi{x}\right)\left(\varphi\right)^{−{x}} −\mathrm{1}\right)\sqrt{{F}\left({x}\right)\sqrt{\mathrm{5}}+{cos}\left(\pi{x}\right)\left(\varphi\right)^{−{x}} −\mathrm{1}}}{dx} \\ $$$$ \\ $$$${F}\left({x}\right)={Fib}\left({x}\right)={xth}\:{Extended}\:{fibonacci}\:{number} \\ $$$${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$$\varphi=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$

Question Number 98773 Answers: 2 Comments: 0

if x is a selected number of the number from 20−99, then what is probalility x^3 −x is divided by 12?

$$\mathrm{if}\:\mathrm{x}\:\mathrm{is}\:\mathrm{a}\:\mathrm{selected}\:\mathrm{number}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{from}\:\mathrm{20}−\mathrm{99},\:\mathrm{then}\:\mathrm{what} \\ $$$$\mathrm{is}\:\mathrm{probalility}\:\mathrm{x}^{\mathrm{3}} −\mathrm{x}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by} \\ $$$$\mathrm{12}?\: \\ $$

Question Number 98770 Answers: 0 Comments: 2

Question Number 98768 Answers: 2 Comments: 0

lim_(x→0) (((√(x+1)) sin x+ln(1+x^2 )−x)/(((1+x^2 ))^(1/(3 )) −1))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}+\mathrm{1}}\:\mathrm{sin}\:\mathrm{x}+\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)−\mathrm{x}}{\sqrt[{\mathrm{3}\:\:}]{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }−\mathrm{1}} \\ $$

Question Number 98761 Answers: 0 Comments: 5

(√(x+(√x) )) −(√(x−(√x))) = m(√(x/(x+(√x)))) m is a real parameter

$$\sqrt{\mathrm{x}+\sqrt{\mathrm{x}}\:}\:−\sqrt{\mathrm{x}−\sqrt{\mathrm{x}}}\:=\:\mathrm{m}\sqrt{\frac{\mathrm{x}}{\mathrm{x}+\sqrt{\mathrm{x}}}} \\ $$$$\mathrm{m}\:\mathrm{is}\:\mathrm{a}\:\mathrm{real}\:\mathrm{parameter} \\ $$

Pg 1175 Pg 1176 Pg 1177 Pg 1178 Pg 1179 Pg 1180 Pg 1181 Pg 1182 Pg 1183 Pg 1184

Terms of Service

Contact: info@tinkutara.com