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Question Number 158494 Answers: 0 Comments: 0

Question Number 158492 Answers: 1 Comments: 0

∫ (dx/(1+x^7 )) ?

$$\:\int\:\frac{\mathrm{dx}}{\mathrm{1}+\mathrm{x}^{\mathrm{7}} }\:? \\ $$

Question Number 158489 Answers: 0 Comments: 0

find the partial derivatives of the function with respect to each variable f(x,y)=∫_x ^y g(t) dt

$${find}\:{the}\:{partial}\:{derivatives}\:{of}\:{the}\:{function} \\ $$$${with}\:{respect}\:{to}\:{each}\:{variable} \\ $$$${f}\left({x},{y}\right)=\int_{{x}} ^{{y}} {g}\left({t}\right)\:{dt} \\ $$

Question Number 158483 Answers: 0 Comments: 0

Question Number 158482 Answers: 0 Comments: 0

Question Number 158519 Answers: 0 Comments: 0

Question Number 158477 Answers: 2 Comments: 0

I_(n ) =∫_0 ^1 (x^(2n+1) /( (√(1+x^2 ))))dx , n≥0 prove that ∀ n≥0 (2n+1)I_n =(√2)−2nI_(n−1)

$${I}_{{n}\:} =\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{2}{n}+\mathrm{1}} }{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx}\:,\:{n}\geqslant\mathrm{0}\: \\ $$$${prove}\:{that}\:\forall\:{n}\geqslant\mathrm{0}\: \\ $$$$\left(\mathrm{2}{n}+\mathrm{1}\right){I}_{{n}} =\sqrt{\mathrm{2}}−\mathrm{2}{nI}_{{n}−\mathrm{1}} \\ $$

Question Number 158529 Answers: 1 Comments: 0

In how many ways can 30 students be distributed to 10 schools, if 1. each school should get at least one student. 2. no restriction

$${In}\:{how}\:{many}\:{ways}\:{can}\:\mathrm{30}\:{students} \\ $$$${be}\:{distributed}\:{to}\:\mathrm{10}\:{schools},\:{if} \\ $$$$\mathrm{1}.\:{each}\:{school}\:{should}\:{get}\:{at}\:{least}\:{one} \\ $$$$\:\:\:\:\:{student}. \\ $$$$\mathrm{2}.\:{no}\:{restriction} \\ $$

Question Number 158528 Answers: 0 Comments: 0

Π_(n=1) ^∞ ((((n+1)^3 −1)/((n+1)^3 +1)))=?

$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\left(\boldsymbol{\mathrm{n}}+\mathrm{1}\right)^{\mathrm{3}} −\mathrm{1}}{\left(\boldsymbol{\mathrm{n}}+\mathrm{1}\right)^{\mathrm{3}} +\mathrm{1}}\right)=? \\ $$

Question Number 158472 Answers: 1 Comments: 1

Question Number 158469 Answers: 2 Comments: 0

find the maclaurin series expension for the function f(x) = sin^2 x ; x_o = 0

$${find}\:{the}\:{maclaurin}\:{series}\:{expension} \\ $$$${for}\:{the}\:{function}\:{f}\left({x}\right)\:=\:{sin}^{\mathrm{2}} {x}\:;\:\:\:\:\:\:{x}_{{o}} =\:\mathrm{0} \\ $$

Question Number 158465 Answers: 1 Comments: 0

Question Number 158455 Answers: 1 Comments: 0

Question Number 158450 Answers: 0 Comments: 0

Demontrer que minN=0

$$\mathrm{Demontrer}\:\mathrm{que}\:\mathrm{min}\mathbb{N}=\mathrm{0} \\ $$

Question Number 158444 Answers: 1 Comments: 5

if x and y are positive integers with ((2010)/(2011)) < (x/y) < ((2011)/(2012)) then compute the minimum value for x+y and the values of x and y which achieves this minimum

$$\mathrm{if}\:\:\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}}\:\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{with} \\ $$$$\frac{\mathrm{2010}}{\mathrm{2011}}\:<\:\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{y}}}\:<\:\frac{\mathrm{2011}}{\mathrm{2012}}\:\:\mathrm{then}\:\mathrm{compute}\:\mathrm{the} \\ $$$$\mathrm{minimum}\:\mathrm{value}\:\mathrm{for}\:\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\:\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{values}\:\mathrm{of}\:\:\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}}\:\:\mathrm{which}\:\mathrm{achieves} \\ $$$$\mathrm{this}\:\mathrm{minimum} \\ $$

Question Number 158443 Answers: 1 Comments: 0

How many divisors has the positive integer n which verify n^n = 2027^(2027^(2028) ) ?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{divisors}\:\mathrm{has}\:\mathrm{the}\:\mathrm{positive} \\ $$$$\mathrm{integer}\:\:\boldsymbol{\mathrm{n}}\:\:\mathrm{which}\:\mathrm{verify} \\ $$$$\mathrm{n}^{\boldsymbol{\mathrm{n}}} \:=\:\mathrm{2027}^{\mathrm{2027}^{\mathrm{2028}} } \:? \\ $$

Question Number 158438 Answers: 1 Comments: 2

Question Number 158437 Answers: 0 Comments: 0

Question Number 158410 Answers: 2 Comments: 0

Question Number 158405 Answers: 2 Comments: 0

prove: ∫_0 ^∞ (1/(x^5 +x^4 +x^3 +x^2 +x+1))dx=(π/(3(√3)))

$${prove}: \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{{x}^{\mathrm{5}} +{x}^{\mathrm{4}} +{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx}=\frac{\pi}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$

Question Number 158403 Answers: 0 Comments: 0

Question Number 158402 Answers: 0 Comments: 0

∫_((1;π)) ^((2;π)) (1−(y^2 /x^2 )cos((y/x)))dx+(sin((y/x))+(y/x)cos((y/x)))dy=?

$$\int_{\left(\mathrm{1};\pi\right)} ^{\left(\mathrm{2};\pi\right)} \left(\mathrm{1}−\frac{{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} }{cos}\left(\frac{{y}}{{x}}\right)\right){dx}+\left({sin}\left(\frac{{y}}{{x}}\right)+\frac{{y}}{{x}}{cos}\left(\frac{{y}}{{x}}\right)\right){dy}=? \\ $$

Question Number 158417 Answers: 1 Comments: 0

z^3 −(7+6i)z^2 +3(1+9i)z+2(7−9i)=0 Resolve the equation (E) sachet that the stop image one any solution behoves thru the righ t equation y=x

$${z}^{\mathrm{3}} −\left(\mathrm{7}+\mathrm{6}{i}\right){z}^{\mathrm{2}} +\mathrm{3}\left(\mathrm{1}+\mathrm{9}{i}\right){z}+\mathrm{2}\left(\mathrm{7}−\mathrm{9}{i}\right)=\mathrm{0} \\ $$$${Resolve}\:{the}\:{equation}\:\left({E}\right)\:{sachet}\:{that}\: \\ $$$${the}\:{stop}\:{image}\:\:{one}\:{any}\:{solution}\:{behoves} \\ $$$${thru}\:{the}\:{righ}\:{t}\:{equation}\:{y}={x} \\ $$

Question Number 158420 Answers: 1 Comments: 0

∫_0 ^∞ ((lnx)/(1−x^2 ))dx

$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{lnx}}{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 158419 Answers: 0 Comments: 0

Question Number 158396 Answers: 1 Comments: 0

Any proof or Idea about; (4/2)÷((16)/3) = (4/2)×(3/(16))

$${Any}\:{proof}\:{or}\:{Idea}\:{about}; \\ $$$$\frac{\mathrm{4}}{\mathrm{2}}\boldsymbol{\div}\frac{\mathrm{16}}{\mathrm{3}}\:=\:\frac{\mathrm{4}}{\mathrm{2}}×\frac{\mathrm{3}}{\mathrm{16}} \\ $$

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