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Question Number 98943 Answers: 2 Comments: 0

let f(x) =(1/((1+x^2 )^3 )) developp f at integr serie

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{1}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$

Question Number 98942 Answers: 3 Comments: 2

calculate ∫ ((x+1−(√(2x+3)))/(x−2 +(√(x+1)))) dx

$$\mathrm{calculate}\:\int\:\frac{\mathrm{x}+\mathrm{1}−\sqrt{\mathrm{2x}+\mathrm{3}}}{\mathrm{x}−\mathrm{2}\:+\sqrt{\mathrm{x}+\mathrm{1}}}\:\mathrm{dx} \\ $$

Question Number 98940 Answers: 2 Comments: 1

if (1/((1+x)^n )) =Σ_(m=0) ^∞ a_m x^m determinate a_m

$$\mathrm{if}\:\frac{\mathrm{1}}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{n}} }\:=\sum_{\mathrm{m}=\mathrm{0}} ^{\infty} \:\mathrm{a}_{\mathrm{m}} \mathrm{x}^{\mathrm{m}} \:\:\:\:\mathrm{determinate}\:\mathrm{a}_{\mathrm{m}} \\ $$

Question Number 98932 Answers: 0 Comments: 0

Question Number 98929 Answers: 0 Comments: 6

Find[]the[]integral[]of[] ∫(dt/(√((1+t^(10) ))))

$${Find}\left[\right]{the}\left[\right]{integral}\left[\right]{of}\left[\right] \\ $$$$ \\ $$$$\int\frac{{dt}}{\sqrt{\left(\mathrm{1}+{t}^{\mathrm{10}} \right)}} \\ $$

Question Number 98925 Answers: 1 Comments: 1

If the curve shown below has the equation, y=(x−p)(x^3 −bx−c) then find q/p in terms of b and c.

$${If}\:{the}\:{curve}\:{shown}\:{below}\:{has}\:{the}\: \\ $$$${equation},\:\:{y}=\left({x}−{p}\right)\left({x}^{\mathrm{3}} −{bx}−{c}\right) \\ $$$${then}\:{find}\:\:{q}/{p}\:\:{in}\:{terms}\:{of}\:{b}\:{and}\:{c}. \\ $$

Question Number 98924 Answers: 0 Comments: 0

Prove that if a+ bi is a root to pz^2 + qz + r = 0 , where a,b,p,q,r ∈R then a−bi is also a root to that equation.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:{a}+\:{bi}\:\mathrm{is}\:\mathrm{a}\:\mathrm{root}\:\mathrm{to} \\ $$$$\:{pz}^{\mathrm{2}} \:+\:{qz}\:+\:{r}\:=\:\mathrm{0}\:,\:\mathrm{where}\:{a},{b},{p},{q},{r}\:\in\mathbb{R} \\ $$$$\mathrm{then}\:{a}−{bi}\:\mathrm{is}\:\mathrm{also}\:\mathrm{a}\:\mathrm{root}\:\mathrm{to}\:\mathrm{that}\:\mathrm{equation}. \\ $$

Question Number 98938 Answers: 2 Comments: 0

Question Number 98919 Answers: 0 Comments: 1

Question Number 98914 Answers: 3 Comments: 2

2x+3y=5 (x^2 +y^2 )_(min) =?

$$\mathrm{2}{x}+\mathrm{3}{y}=\mathrm{5} \\ $$$$\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \underset{{min}} {\right)}=? \\ $$

Question Number 98913 Answers: 0 Comments: 3

solve f ′(x)=f(f(x))

$${solve} \\ $$$${f}\:'\left({x}\right)={f}\left({f}\left({x}\right)\right) \\ $$

Question Number 98907 Answers: 1 Comments: 0

Question Number 98895 Answers: 2 Comments: 0

Is (dy/dx) if y^3 +x^3 −2x=1 ?

$${Is}\:\frac{{dy}}{{dx}}\:{if}\:{y}^{\mathrm{3}} +{x}^{\mathrm{3}} −\mathrm{2}{x}=\mathrm{1}\:?\: \\ $$

Question Number 99173 Answers: 1 Comments: 0

Question Number 98887 Answers: 0 Comments: 0

Question Number 98885 Answers: 0 Comments: 2

find the range f(x)=log_4 log_2 log_(1/2) (x)

$${find}\:{the}\:{range} \\ $$$$ \\ $$$${f}\left({x}\right)={log}_{\mathrm{4}} {log}_{\mathrm{2}} {log}_{\frac{\mathrm{1}}{\mathrm{2}}} \left({x}\right) \\ $$

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