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Question Number 104789 Answers: 0 Comments: 1

if y^((n)) is the derivative of the function y of the order n, then ∫y^((n)) dx =........

$${if}\:{y}^{\left({n}\right)} \:{is}\:{the}\:{derivative}\:{of}\:{the}\:{function}\:{y} \\ $$$${of}\:{the}\:{order}\:{n},\:{then} \\ $$$$\int{y}^{\left({n}\right)} {dx}\:=........ \\ $$

Question Number 104783 Answers: 2 Comments: 0

find (d^n y/dx^n ) for f(x)^ =(1/(√(1−x)))

$${find}\:\frac{{d}^{{n}} {y}}{{dx}^{{n}} }\:{for}\:\:\:\:{f}\left({x}\overset{} {\right)}=\frac{\mathrm{1}}{\sqrt{\mathrm{1}−{x}}} \\ $$

Question Number 104782 Answers: 1 Comments: 0

Question Number 104780 Answers: 1 Comments: 2

Question Number 104777 Answers: 3 Comments: 0

Question Number 104775 Answers: 0 Comments: 0

let P_n an n-polynomial. let a_1 ,...,a_n its simple roots let m_k the slope of the tangent to P_n at the point (a_k ,0) prove that Σ_(k=1) ^n (1/m_k )=0 what about multiple roots?

$${let}\:{P}_{{n}} \:{an}\:{n}-{polynomial}. \\ $$$${let}\:{a}_{\mathrm{1}} ,...,{a}_{{n}} \:{its}\:{simple}\:{roots}\: \\ $$$${let}\:{m}_{{k}} \:{the}\:{slope}\:{of}\:{the}\:{tangent}\:{to}\:{P}_{{n}} \:{at} \\ $$$${the}\:{point}\:\left({a}_{{k}} ,\mathrm{0}\right) \\ $$$${prove}\:{that} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{m}_{{k}} }=\mathrm{0} \\ $$$${what}\:{about}\:{multiple}\:{roots}? \\ $$$$ \\ $$

Question Number 104773 Answers: 1 Comments: 0

let A_n =∫∫_([0,n[^2 ) (e^(−x^2 −y^2 ) /(√(x^2 +y^2 )))dxdy 1) calculste A_n interm of n 2) find lim_(n→+∞) A_n

$$\mathrm{let}\:\mathrm{A}_{\mathrm{n}} =\int\int_{\left[\mathrm{0},\mathrm{n}\left[^{\mathrm{2}} \right.\right.} \:\:\:\:\frac{\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} } }{\sqrt{\mathrm{x}^{\mathrm{2}} \:+\mathrm{y}^{\mathrm{2}} }}\mathrm{dxdy} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculste}\:\mathrm{A}_{\mathrm{n}} \:\mathrm{interm}\:\mathrm{of}\:\mathrm{n} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \mathrm{A}_{\mathrm{n}} \\ $$

Question Number 104772 Answers: 2 Comments: 0

let ϕ(x) = x^3 +x+1 1) prove that ϕ have one real root α 2)determine a approximate value for α by use of newton method 3)factorise inside R(x) f(x) 4) calculste ∫ (dx/(ϕ(x)))

$$\mathrm{let}\:\varphi\left(\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{3}} \:+\mathrm{x}+\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{prove}\:\mathrm{that}\:\varphi\:\mathrm{have}\:\mathrm{one}\:\mathrm{real}\:\mathrm{root}\:\alpha \\ $$$$\left.\mathrm{2}\right)\mathrm{determine}\:\mathrm{a}\:\mathrm{approximate}\:\mathrm{value}\:\mathrm{for}\:\alpha\:\:\mathrm{by}\:\mathrm{use}\:\mathrm{of}\:\mathrm{newton}\:\mathrm{method} \\ $$$$\left.\mathrm{3}\right)\mathrm{factorise}\:\mathrm{inside}\:\mathrm{R}\left(\mathrm{x}\right)\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\left.\mathrm{4}\right)\:\mathrm{calculste}\:\int\:\frac{\mathrm{dx}}{\varphi\left(\mathrm{x}\right)} \\ $$

Question Number 104771 Answers: 1 Comments: 0

let f(x) =x^3 +x−3 1) prove that f have one root real α_0 and α_0 ∈ ]1,2[ 2) factorize f(x) inside R[x] and C[x] 3 ) find ∫ (dx/(f(x)))

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{x}^{\mathrm{3}} \:+\mathrm{x}−\mathrm{3} \\ $$$$\left.\mathrm{1}\left.\right)\:\mathrm{prove}\:\mathrm{that}\:\mathrm{f}\:\mathrm{have}\:\mathrm{one}\:\mathrm{root}\:\mathrm{real}\:\alpha_{\mathrm{0}} \:\:\:\mathrm{and}\:\alpha_{\mathrm{0}} \:\in\:\right]\mathrm{1},\mathrm{2}\left[\right. \\ $$$$\left.\mathrm{2}\right)\:\mathrm{factorize}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{inside}\:\mathrm{R}\left[\mathrm{x}\right]\:\mathrm{and}\:\mathrm{C}\left[\mathrm{x}\right] \\ $$$$\left.\mathrm{3}\:\right)\:\mathrm{find}\:\int\:\frac{\mathrm{dx}}{\mathrm{f}\left(\mathrm{x}\right)} \\ $$

Question Number 104769 Answers: 1 Comments: 1

Question Number 104768 Answers: 1 Comments: 0

((1/8)÷(1/8))((1/7)÷(1/7))((2/3)÷(2/3))= ?

$$\left(\frac{\mathrm{1}}{\mathrm{8}}\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{8}}\right)\left(\frac{\mathrm{1}}{\mathrm{7}}\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{7}}\right)\left(\frac{\mathrm{2}}{\mathrm{3}}\boldsymbol{\div}\frac{\mathrm{2}}{\mathrm{3}}\right)=\:? \\ $$

Question Number 104774 Answers: 1 Comments: 0

let B_n = ∫∫_([0,n[^2 ) ((arctan(x^2 +3y^2 ))/(√(x^2 +3y^2 )))dxdy calculate lim_(n→+∞) (B_n /n)

$$\mathrm{let}\:\mathrm{B}_{\mathrm{n}} =\:\int\int_{\left[\mathrm{0},\mathrm{n}\left[^{\mathrm{2}} \right.\right.} \:\:\:\frac{\mathrm{arctan}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3y}^{\mathrm{2}} \right)}{\sqrt{\mathrm{x}^{\mathrm{2}} \:+\mathrm{3y}^{\mathrm{2}} }}\mathrm{dxdy} \\ $$$$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\frac{\mathrm{B}_{\mathrm{n}} }{\mathrm{n}} \\ $$

Question Number 104761 Answers: 0 Comments: 1

A box contains 5 white balls, 3 black balls and 2 red balls of the same size. A ball is selected at random from the box and then replaced. A second ball is then selected. Find the probability of obtaining one black ball or red ball in any order

$$ \\ $$$$\:\:\mathrm{A}\:\mathrm{box}\:\mathrm{contains}\:\mathrm{5}\:\mathrm{white}\:\mathrm{balls},\:\mathrm{3}\:\mathrm{black} \\ $$$$\mathrm{balls}\:\mathrm{and}\:\mathrm{2}\:\mathrm{red}\:\mathrm{balls}\:\mathrm{of}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{size}.\:\mathrm{A}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{selected}\:\mathrm{at}\:\mathrm{random} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{box}\:\mathrm{and}\:\mathrm{then}\:\mathrm{replaced}.\:\mathrm{A} \\ $$$$\mathrm{second}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{then}\:\mathrm{selected}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{obtaining}\: \\ $$$$\:\mathrm{one}\:\mathrm{black}\:\mathrm{ball}\:\mathrm{or}\:\mathrm{red}\:\mathrm{ball}\:\mathrm{in}\:\mathrm{any} \\ $$$$\mathrm{order} \\ $$

Question Number 104760 Answers: 1 Comments: 0

Question Number 104759 Answers: 1 Comments: 0

Question Number 104758 Answers: 0 Comments: 0

Question Number 104752 Answers: 1 Comments: 1

Question Number 104751 Answers: 1 Comments: 0

Question Number 104746 Answers: 2 Comments: 0

lim_(x→∞) (((1/2))^(3x) +((1/2))^x )^(1/x^2 )

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{3}{x}} +\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{{x}} \right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} \: \\ $$

Question Number 104744 Answers: 0 Comments: 0

ABCD is a square with center O. I is the middle of [BC]. 1) q is geometric transformation defined by q: M→M′ such that CM′^(→) =CM^(→) +3DM^(→) . a)Determinate the invariant point of q. b) show that q is a homothety and precise it ratio.

$${ABCD}\:{is}\:{a}\:{square}\:{with}\:{center}\:{O}. \\ $$$${I}\:{is}\:{the}\:{middle}\:{of}\:\left[{BC}\right]. \\ $$$$\left.\mathrm{1}\right)\:{q}\:{is}\:{geometric}\:{transformation} \\ $$$${defined}\:{by}\:{q}:\:{M}\rightarrow{M}'\:{such}\:{that} \\ $$$$\overset{\rightarrow} {{CM}'}=\overset{\rightarrow} {{CM}}+\mathrm{3}\overset{\rightarrow} {{DM}}. \\ $$$$\left.{a}\right){Determinate}\:{the}\:{invariant}\:{point} \\ $$$${of}\:{q}. \\ $$$$\left.{b}\right)\:{show}\:{that}\:{q}\:{is}\:{a}\:{homothety}\:{and}\: \\ $$$${precise}\:{it}\:{ratio}. \\ $$

Question Number 104735 Answers: 1 Comments: 2

Question Number 104732 Answers: 0 Comments: 0

∫_0 ^1 log(tanθ)dθ

$$\int_{\mathrm{0}} ^{\mathrm{1}} {log}\left({tan}\theta\right){d}\theta \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 104811 Answers: 2 Comments: 0

Given { ((a+b(√3)−2c = 1)),((3b^2 +c^2 = 2a^2 )),((a^2 +4ac = 5c^2 )) :} find b

$${Given}\:\begin{cases}{{a}+{b}\sqrt{\mathrm{3}}−\mathrm{2}{c}\:=\:\mathrm{1}}\\{\mathrm{3}{b}^{\mathrm{2}} +{c}^{\mathrm{2}} \:=\:\mathrm{2}{a}^{\mathrm{2}} }\\{{a}^{\mathrm{2}} +\mathrm{4}{ac}\:=\:\mathrm{5}{c}^{\mathrm{2}} }\end{cases} \\ $$$${find}\:{b} \\ $$

Question Number 104727 Answers: 4 Comments: 1

Given x + (1/x) = 2cos θ find x^n +(1/x^n ) = ?

$$\mathcal{G}{iven}\:{x}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{2cos}\:\theta \\ $$$${find}\:{x}^{{n}} +\frac{\mathrm{1}}{{x}^{{n}} }\:=\:? \\ $$

Question Number 104718 Answers: 2 Comments: 0

∫tan^(−1) (((a(√x)+b)/c))dx

$$\int{tan}^{−\mathrm{1}} \left(\frac{{a}\sqrt{{x}}+{b}}{{c}}\right){dx}\: \\ $$

Question Number 104717 Answers: 0 Comments: 0

In the a sport camp, 65% children know playing the football,70%−in voleyball,75%−in basketball.What is least number of children who know playing all above three sport games? (Answer 10%)

$$\mathrm{In}\:\mathrm{the}\:\mathrm{a}\:\:\mathrm{sport}\:\mathrm{camp},\:\mathrm{65\%}\:\mathrm{children}\:\mathrm{know} \\ $$$$\mathrm{playing}\:\mathrm{the}\:\mathrm{football},\mathrm{70\%}−\mathrm{in}\:\mathrm{voleyball},\mathrm{75\%}−\mathrm{in} \\ $$$$\mathrm{basketball}.\mathrm{What}\:\mathrm{is}\:\mathrm{least}\:\mathrm{number}\:\mathrm{of}\:\mathrm{children}\:\mathrm{who} \\ $$$$\mathrm{know}\:\mathrm{playing}\:\mathrm{all}\:\mathrm{above}\:\mathrm{three}\:\mathrm{sport}\:\mathrm{games}? \\ $$$$\left(\mathrm{Answer}\:\mathrm{10\%}\right) \\ $$

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