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Question Number 104856 Answers: 1 Comments: 0

lim_(z→0) (z^− /z) , lim_(z→i) (((z^− )^4 )/z^4 ) ,lim_(z→0) ((sinz)/z)

$$\underset{{z}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\overset{−} {{z}}}{{z}}\:\:\:\:,\:\:\:\:\underset{{z}\rightarrow{i}} {\mathrm{lim}}\:\frac{\left(\overset{−} {{z}}\right)^{\mathrm{4}} }{{z}^{\mathrm{4}} }\:\:,\underset{{z}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{sinz}}{{z}}\: \\ $$

Question Number 104845 Answers: 1 Comments: 0

solve y′ = y−x−1+(x−y+2)^(−1)

$${solve}\:{y}'\:=\:{y}−{x}−\mathrm{1}+\left({x}−{y}+\mathrm{2}\right)^{−\mathrm{1}} \\ $$

Question Number 104841 Answers: 3 Comments: 3

Question Number 104838 Answers: 1 Comments: 0

lim_(x→0) ((cos ^3 (8x)−1)/(6x^2 )) ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\:^{\mathrm{3}} \left(\mathrm{8}{x}\right)−\mathrm{1}}{\mathrm{6}{x}^{\mathrm{2}} }\:? \\ $$

Question Number 104835 Answers: 2 Comments: 0

{ ((log _p (q) = x^2 )),((log _q (p^3 ) = x )) :} find x

$$\begin{cases}{\mathrm{log}\:_{{p}} \left({q}\right)\:=\:{x}^{\mathrm{2}} }\\{\mathrm{log}\:_{{q}} \left({p}^{\mathrm{3}} \right)\:=\:{x}\:}\end{cases} \\ $$$${find}\:{x}\: \\ $$

Question Number 104832 Answers: 1 Comments: 0

{ ((x+y+(x^2 /y^2 ) = 7)),(((((x−y)x^2 )/y^2 ) = 12 )) :}

$$\begin{cases}{{x}+{y}+\frac{{x}^{\mathrm{2}} }{{y}^{\mathrm{2}} }\:=\:\mathrm{7}}\\{\frac{\left({x}−{y}\right){x}^{\mathrm{2}} }{{y}^{\mathrm{2}} }\:=\:\mathrm{12}\:}\end{cases} \\ $$

Question Number 104826 Answers: 1 Comments: 1

∫3^(x+2) ∙lnsin3^x dx=???

$$\int\mathrm{3}^{{x}+\mathrm{2}} \centerdot{lnsin}\mathrm{3}^{{x}} {dx}=??? \\ $$

Question Number 104821 Answers: 2 Comments: 0

3+8+15+24+35+... find sum of 50^(th) −term

$$\mathrm{3}+\mathrm{8}+\mathrm{15}+\mathrm{24}+\mathrm{35}+...\: \\ $$$${find}\:{sum}\:{of}\:\mathrm{50}^{{th}} −{term}\: \\ $$

Question Number 104812 Answers: 1 Comments: 0

lim_(x→∞) ((((3/x)))/(((2/x)+5)^2 −25)) ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\left(\frac{\mathrm{3}}{{x}}\right)}{\left(\frac{\mathrm{2}}{{x}}+\mathrm{5}\right)^{\mathrm{2}} −\mathrm{25}}\:? \\ $$

Question Number 104799 Answers: 0 Comments: 1

Question Number 104796 Answers: 1 Comments: 2

show that 8cos^4 x−8cos^2 x+1=cos4x.

$${show}\:{that}\: \\ $$$$\mathrm{8}{cos}^{\mathrm{4}} {x}−\mathrm{8}{cos}^{\mathrm{2}} {x}+\mathrm{1}={cos}\mathrm{4}{x}. \\ $$

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

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