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Question Number 171146 Answers: 0 Comments: 2

Question Number 171145 Answers: 0 Comments: 0

let p be a non constant polynomial with degree n such that: p(z)=a_n z^n +...+a_0 show that if z∈C with∣z∣≥max{1,(2/(∣a_n ∣))Σ_(i=1) ^(n−1) ∣a_i ∣} then (1/2)∣a_n ∣∣z∣^n ≤∣p(z)∣≤(3/2)∣a_n ∣∣z∣^n (i already did the right side of the inequality so try to show ∣p(z)∣≥(1/2)∣a_n ∣∣z∣^n )

$$\mathrm{let}\:\mathrm{p}\:\mathrm{be}\:\mathrm{a}\:\mathrm{non}\:\mathrm{constant}\:\mathrm{polynomial}\:\mathrm{with}\: \\ $$$$\mathrm{degree}\:\mathrm{n}\:\mathrm{such}\:\mathrm{that}:\:\mathrm{p}\left(\mathrm{z}\right)=\mathrm{a}_{\mathrm{n}} \mathrm{z}^{\mathrm{n}} +...+\mathrm{a}_{\mathrm{0}} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{if}\:\mathrm{z}\in\mathbb{C}\:\mathrm{with}\mid\mathrm{z}\mid\geqslant\mathrm{max}\left\{\mathrm{1},\frac{\mathrm{2}}{\mid\mathrm{a}_{\mathrm{n}} \mid}\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\mid\mathrm{a}_{\mathrm{i}} \mid\right\} \\ $$$$\mathrm{then}\:\frac{\mathrm{1}}{\mathrm{2}}\mid\mathrm{a}_{\mathrm{n}} \mid\mid\mathrm{z}\mid^{\mathrm{n}} \leqslant\mid\mathrm{p}\left(\mathrm{z}\right)\mid\leqslant\frac{\mathrm{3}}{\mathrm{2}}\mid\mathrm{a}_{\mathrm{n}} \mid\mid\mathrm{z}\mid^{\mathrm{n}} \\ $$$$\left(\mathrm{i}\:\mathrm{already}\:\mathrm{did}\:\mathrm{the}\:\mathrm{right}\:\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{inequality}\right. \\ $$$$\left.\mathrm{so}\:\mathrm{try}\:\mathrm{to}\:\mathrm{show}\:\mid\mathrm{p}\left(\mathrm{z}\right)\mid\geqslant\frac{\mathrm{1}}{\mathrm{2}}\mid\mathrm{a}_{\mathrm{n}} \mid\mid\mathrm{z}\mid^{\mathrm{n}} \right) \\ $$

Question Number 171136 Answers: 0 Comments: 4

Using Taylor′s theorem, prove that x−(x^3 /6)<sin x<x−(x^3 /6)+(x^5 /(120)) for x>0

$$\mathrm{Using}\:\mathrm{Taylor}'\mathrm{s}\:\mathrm{theorem},\:\mathrm{prove}\:\mathrm{that} \\ $$$${x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}<\mathrm{sin}\:{x}<{x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}+\frac{{x}^{\mathrm{5}} }{\mathrm{120}}\:\:\:\mathrm{for}\:{x}>\mathrm{0} \\ $$

Question Number 171134 Answers: 0 Comments: 0

Question Number 171132 Answers: 1 Comments: 0

Question Number 171130 Answers: 0 Comments: 0

Question Number 171125 Answers: 1 Comments: 0

Question Number 171124 Answers: 0 Comments: 0

Question Number 171117 Answers: 3 Comments: 0

∫_0 ^∞ ((sin x)/x)dx = (?)

$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{sin}\:{x}}{{x}}{dx}\:=\:\left(?\right) \\ $$

Question Number 171116 Answers: 0 Comments: 0

Question Number 171109 Answers: 2 Comments: 1

Question Number 171108 Answers: 1 Comments: 0

Question Number 171107 Answers: 0 Comments: 0

Please help lim_(x→−∞) (x−1)e^(x−1) −1=? lim_(x→+∞) (x−1)e^(x−1) −1=? g(x)=(x−1)e^(x−1) −1 g(x)′=?

$${Please}\:{help} \\ $$$${li}\underset{{x}\rightarrow−\infty} {{m}}\left({x}−\mathrm{1}\right){e}^{{x}−\mathrm{1}} −\mathrm{1}=? \\ $$$${li}\underset{{x}\rightarrow+\infty} {{m}}\left({x}−\mathrm{1}\right){e}^{{x}−\mathrm{1}} −\mathrm{1}=? \\ $$$${g}\left({x}\right)=\left({x}−\mathrm{1}\right){e}^{{x}−\mathrm{1}} −\mathrm{1} \\ $$$${g}\left({x}\right)'=? \\ $$$$ \\ $$

Question Number 171096 Answers: 1 Comments: 0

∫((x e^(2x) )/((2x+1)^2 ))dx please help

$$ \\ $$$$\int\frac{{x}\:{e}^{\mathrm{2}{x}} }{\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx}\:\:\:\:{please}\:{help} \\ $$

Question Number 171094 Answers: 0 Comments: 0

prove that: 𝛀=Σ_(n=0) ^∞ ((((n!)^2 )/((2n)!)))^2 (2^(4n) /((2n+1)^3 ))=^? (7/2)𝛇(3)−πG G−Catalan′s constant

$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}: \\ $$$$\boldsymbol{\Omega}=\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\left(\boldsymbol{\mathrm{n}}!\right)^{\mathrm{2}} }{\left(\mathrm{2}\boldsymbol{\mathrm{n}}\right)!}\right)^{\mathrm{2}} \frac{\mathrm{2}^{\mathrm{4}\boldsymbol{\mathrm{n}}} }{\left(\mathrm{2}\boldsymbol{\mathrm{n}}+\mathrm{1}\right)^{\mathrm{3}} }\overset{?} {=}\frac{\mathrm{7}}{\mathrm{2}}\boldsymbol{\zeta}\left(\mathrm{3}\right)−\pi\boldsymbol{\mathrm{G}} \\ $$$$\boldsymbol{\mathrm{G}}−\boldsymbol{\mathrm{Catalan}}'\boldsymbol{\mathrm{s}}\:\:\boldsymbol{\mathrm{constant}} \\ $$

Question Number 171091 Answers: 0 Comments: 2

Question Number 171090 Answers: 1 Comments: 3

I_n =∫_0 ^1 (1−u)(√(ud(u))) Demonstrate that ∀n∈N, I_(n+1) −I_n =(1−u)^n u^(3/2) d(u) and deduce the meaning of variations of (I_n )∈N

$${I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{u}\right)\sqrt{{ud}\left({u}\right)} \\ $$$${Demonstrate}\:{that}\:\forall{n}\in{N},\:{I}_{{n}+\mathrm{1}} −{I}_{{n}} =\left(\mathrm{1}−{u}\right)^{{n}} {u}^{\frac{\mathrm{3}}{\mathrm{2}}} {d}\left({u}\right)\:\:{and}\:{deduce}\:{the}\:{meaning}\:{of}\:{variations}\:{of}\:\left({I}_{{n}} \right)\in{N} \\ $$

Question Number 171085 Answers: 1 Comments: 0

43 devided by x remainder is x−5 how many value of x?

$$\mathrm{43}\:{devided}\:{by}\:{x}\:{remainder}\:{is}\:{x}−\mathrm{5}\:{how}\:{many}\:{value}\:{of}\:{x}? \\ $$

Question Number 171079 Answers: 1 Comments: 2

lim_(x→0) (((√(1+(√(1+(√(1−x))))))−(√(1+(√(1+(√(1+x)))))))/x)=?

$$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}−{x}}}}−\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+{x}}}}}{{x}}=? \\ $$

Question Number 171078 Answers: 1 Comments: 0

sketch the graph of y=ln(x+5)

$$\boldsymbol{\mathrm{sketch}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{graph}}\:\boldsymbol{\mathrm{of}} \\ $$$$\:\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}+\mathrm{5}\right) \\ $$$$ \\ $$

Question Number 171071 Answers: 1 Comments: 0

justify that ∫_0 ^(+∞) (dt/(1+t^4 )) is convergent.

$${justify}\:{that}\:\int_{\mathrm{0}} ^{+\infty} \frac{{dt}}{\mathrm{1}+{t}^{\mathrm{4}} }\:{is}\:{convergent}. \\ $$

Question Number 171070 Answers: 1 Comments: 0

x^2 −1=2^x find x

$$\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{1}=\mathrm{2}^{\boldsymbol{\mathrm{x}}} \\ $$$$\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{x}} \\ $$

Question Number 171064 Answers: 2 Comments: 0

When A^(−1) = [(3,1),(8,4) ] find the A=? ,∣A^(−1) ∣∙A=?

$${When}\:\:{A}^{−\mathrm{1}} =\begin{bmatrix}{\mathrm{3}}&{\mathrm{1}}\\{\mathrm{8}}&{\mathrm{4}}\end{bmatrix} \\ $$$${find}\:{the}\:\:{A}=?\:,\mid{A}^{−\mathrm{1}} \mid\centerdot{A}=? \\ $$

Question Number 171046 Answers: 2 Comments: 0

Question Number 171044 Answers: 1 Comments: 3

Is the Light a matter?

$${Is}\:{the}\:{Light}\:{a}\:{matter}? \\ $$

Question Number 171043 Answers: 1 Comments: 0

A∈R A=(((√(x−2))+x+3)/( (√(4−2x))+x−1)) faind A=?

$${A}\in{R} \\ $$$${A}=\frac{\sqrt{{x}−\mathrm{2}}+{x}+\mathrm{3}}{\:\sqrt{\mathrm{4}−\mathrm{2}{x}}+{x}−\mathrm{1}}\:\:\:\:\:\:\:\:\:\:{faind}\:{A}=? \\ $$

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