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Question Number 144380 Answers: 1 Comments: 0

L=lim_(n→+∝) ((1/(1^2 +2(1))) + (1/(2^2 +2n)) +...+ (1/(n^2 +2n)))=?

$$\mathrm{L}=\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} +\mathrm{2}\left(\mathrm{1}\right)}\:+\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} +\mathrm{2n}}\:+...+\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{2n}}\right)=? \\ $$

Question Number 144379 Answers: 2 Comments: 0

cos^2 x+tan^2 x=(3/2) xεR

$$\:\:\:\:\:\:\:\:\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{x}\epsilon\mathrm{R}\: \\ $$

Question Number 144374 Answers: 0 Comments: 0

Question Number 144372 Answers: 0 Comments: 0

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Question Number 144373 Answers: 0 Comments: 0

Question Number 144367 Answers: 0 Comments: 1

Question Number 144359 Answers: 1 Comments: 0

∫ ((x^4 e^x dx)/((x^4 +4x^3 +12x^2 +24x+24+72e^x )^2 )) = ?

$$\int\:\frac{{x}^{\mathrm{4}} {e}^{{x}} \:{dx}}{\left({x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{3}} +\mathrm{12}{x}^{\mathrm{2}} +\mathrm{24}{x}+\mathrm{24}+\mathrm{72}{e}^{{x}} \right)^{\mathrm{2}} }\:=\:? \\ $$

Question Number 144353 Answers: 1 Comments: 1

Question Number 144351 Answers: 1 Comments: 0

Evaluate :: 𝛗:=∫_0 ^( ∞) (( sin (x)^(1/( 3 )) )log ((1/x) ))/x)dx=?

$$ \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:{Evaluate}\:\:\::: \\ $$$$\:\: \\ $$$$\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \frac{\left.\:{sin}\:\sqrt[{\:\mathrm{3}\:}]{{x}}\:\right){log}\:\left(\frac{\mathrm{1}}{{x}}\:\right)}{{x}}{dx}=? \\ $$$$\:\:\: \\ $$$$ \\ $$

Question Number 144356 Answers: 1 Comments: 0

y′+cos(x)y=cos^2 x

$$\mathrm{y}'+\mathrm{cos}\left(\mathrm{x}\right)\mathrm{y}=\mathrm{cos}^{\mathrm{2}} \mathrm{x} \\ $$

Question Number 144348 Answers: 1 Comments: 3

Question Number 144342 Answers: 1 Comments: 0

Montrer que ∀n∈Z E(((n−1)/2))+E(((n+2)/4))+E(((n+4)/4))=n

$${Montrer}\:{que}\:\forall{n}\in\mathbb{Z} \\ $$$${E}\left(\frac{{n}−\mathrm{1}}{\mathrm{2}}\right)+{E}\left(\frac{{n}+\mathrm{2}}{\mathrm{4}}\right)+{E}\left(\frac{{n}+\mathrm{4}}{\mathrm{4}}\right)={n} \\ $$

Question Number 144340 Answers: 0 Comments: 0

x^2 +2ab−3=0 x^2 +2ab−3=0 x^2 +2ab−3=0 3

$$ \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{2ab}−\mathrm{3}=\mathrm{0} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{2ab}−\mathrm{3}=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{2ab}−\mathrm{3}=\mathrm{0} \\ $$$$\:\mathrm{3} \\ $$

Question Number 144335 Answers: 0 Comments: 0

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Question Number 144334 Answers: 1 Comments: 0

Reduct it: ((z^8 + z + 1)/(z^5 + z + 1))

$${Reduct}\:{it}:\:\:\frac{\boldsymbol{{z}}^{\mathrm{8}} \:+\:\boldsymbol{{z}}\:+\:\mathrm{1}}{\boldsymbol{{z}}^{\mathrm{5}} \:+\:\boldsymbol{{z}}\:+\:\mathrm{1}} \\ $$

Question Number 144329 Answers: 0 Comments: 2

find the number of solutions of (√(6−cos x+7sin^2 x))+cos x=0

$$\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\: \\ $$$$\mathrm{of}\:\sqrt{\mathrm{6}−\mathrm{cos}\:\mathrm{x}+\mathrm{7sin}^{\mathrm{2}} \mathrm{x}}+\mathrm{cos}\:\mathrm{x}=\mathrm{0} \\ $$

Question Number 144327 Answers: 1 Comments: 0

Give f(x)=x^5 −5x^4 +4x^3 −3x^2 +2x−1,& α= (2)^(1/3) (((5+3(√3)))^(1/3) − ((2)^(1/3) /( ((5+3(√3)))^(1/3) ))).Find f(α)?

$$\mathrm{Give}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{5}} −\mathrm{5x}^{\mathrm{4}} +\mathrm{4x}^{\mathrm{3}} −\mathrm{3x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{1},\& \\ $$$$\alpha=\:\sqrt[{\mathrm{3}}]{\mathrm{2}}\left(\sqrt[{\mathrm{3}}]{\mathrm{5}+\mathrm{3}\sqrt{\mathrm{3}}}−\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{2}}}{\:\sqrt[{\mathrm{3}}]{\mathrm{5}+\mathrm{3}\sqrt{\mathrm{3}}}}\right).\mathrm{Find}\:\mathrm{f}\left(\alpha\right)? \\ $$

Question Number 144323 Answers: 1 Comments: 0

Σ_(i=1) ^n (((−1)^(n+1) )/n)=?

$$\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}+\mathrm{1}} }{\mathrm{n}}=? \\ $$

Question Number 144322 Answers: 1 Comments: 0

Σ_(n=0) ^∞ (((2n)!!)/((2n+1)!!(n+1)))x^(2n+2) =?..........∣x∣≤1

$$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2n}\right)!!}{\left(\mathrm{2n}+\mathrm{1}\right)!!\left(\mathrm{n}+\mathrm{1}\right)}\mathrm{x}^{\mathrm{2n}+\mathrm{2}} =?..........\mid\mathrm{x}\mid\leqslant\mathrm{1} \\ $$

Question Number 144318 Answers: 1 Comments: 0

Question Number 144311 Answers: 2 Comments: 2

......Nice .... Calculus...... Find the value of :: Θ :=Σ_(n =1) ^∞ (1/(4^( n) cos^( 2) ((( π)/( 2^( n + 2) )) ) )) =? ..........

$$ \\ $$$$\:\:\:\:\:\:......\mathrm{Nice}\:\:\:\:....\:\:\:\:\mathrm{Calculus}...... \\ $$$$\:\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\::: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\Theta\::=\underset{{n}\:=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{4}^{\:{n}} \:{cos}^{\:\mathrm{2}} \:\left(\frac{\:\pi}{\:\mathrm{2}^{\:{n}\:+\:\mathrm{2}} }\:\right)\:\:}\:=? \\ $$$$\:\:\:\:.......... \\ $$

Question Number 144333 Answers: 0 Comments: 3

find the number of solutions of 1+ sin x.sin^2 (x/2)=0 in [−Π Π]

$$\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of} \\ $$$$\mathrm{1}+\:\mathrm{sin}\:\mathrm{x}.\mathrm{sin}^{\mathrm{2}} \frac{\mathrm{x}}{\mathrm{2}}=\mathrm{0}\:\mathrm{in}\:\left[−\Pi\:\Pi\right] \\ $$

Question Number 144332 Answers: 0 Comments: 0

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Question Number 144307 Answers: 2 Comments: 1

lim_(n→∞) (1+(1/n))^p

$${lim}_{{n}\rightarrow\infty} \left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{p}} \\ $$

Question Number 144305 Answers: 2 Comments: 0

if (a−b)sin(θ+φ)=(a+b)sin(θ−φ) and a tan(θ/2) − b tan(φ/2) = c then prove that the following i) sinφ = ((2bc)/(a^2 −b^2 −c^2 )) ii) sinθ = ((2ac)/(a^2 −b^2 +c^2 ))

$$\mathrm{if}\:\left(\mathrm{a}−\mathrm{b}\right)\mathrm{sin}\left(\theta+\phi\right)=\left(\mathrm{a}+\mathrm{b}\right)\mathrm{sin}\left(\theta−\phi\right)\: \\ $$$$\mathrm{and}\:\mathrm{a}\:\mathrm{tan}\frac{\theta}{\mathrm{2}}\:−\:\mathrm{b}\:\mathrm{tan}\frac{\phi}{\mathrm{2}}\:=\:\mathrm{c}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{following} \\ $$$$\left.\mathrm{i}\right)\:\mathrm{sin}\phi\:=\:\frac{\mathrm{2bc}}{\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} −\mathrm{c}^{\mathrm{2}} }\: \\ $$$$\left.\mathrm{ii}\right)\:\mathrm{sin}\theta\:=\:\frac{\mathrm{2ac}}{\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} }\: \\ $$

Question Number 144301 Answers: 1 Comments: 0

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