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Question Number 158403 Answers: 0 Comments: 0

Question Number 158402 Answers: 0 Comments: 0

∫_((1;π)) ^((2;π)) (1−(y^2 /x^2 )cos((y/x)))dx+(sin((y/x))+(y/x)cos((y/x)))dy=?

$$\int_{\left(\mathrm{1};\pi\right)} ^{\left(\mathrm{2};\pi\right)} \left(\mathrm{1}−\frac{{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} }{cos}\left(\frac{{y}}{{x}}\right)\right){dx}+\left({sin}\left(\frac{{y}}{{x}}\right)+\frac{{y}}{{x}}{cos}\left(\frac{{y}}{{x}}\right)\right){dy}=? \\ $$

Question Number 158417 Answers: 1 Comments: 0

z^3 −(7+6i)z^2 +3(1+9i)z+2(7−9i)=0 Resolve the equation (E) sachet that the stop image one any solution behoves thru the righ t equation y=x

$${z}^{\mathrm{3}} −\left(\mathrm{7}+\mathrm{6}{i}\right){z}^{\mathrm{2}} +\mathrm{3}\left(\mathrm{1}+\mathrm{9}{i}\right){z}+\mathrm{2}\left(\mathrm{7}−\mathrm{9}{i}\right)=\mathrm{0} \\ $$$${Resolve}\:{the}\:{equation}\:\left({E}\right)\:{sachet}\:{that}\: \\ $$$${the}\:{stop}\:{image}\:\:{one}\:{any}\:{solution}\:{behoves} \\ $$$${thru}\:{the}\:{righ}\:{t}\:{equation}\:{y}={x} \\ $$

Question Number 158420 Answers: 1 Comments: 0

∫_0 ^∞ ((lnx)/(1−x^2 ))dx

$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{lnx}}{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 158419 Answers: 0 Comments: 0

Question Number 158396 Answers: 1 Comments: 0

Any proof or Idea about; (4/2)÷((16)/3) = (4/2)×(3/(16))

$${Any}\:{proof}\:{or}\:{Idea}\:{about}; \\ $$$$\frac{\mathrm{4}}{\mathrm{2}}\boldsymbol{\div}\frac{\mathrm{16}}{\mathrm{3}}\:=\:\frac{\mathrm{4}}{\mathrm{2}}×\frac{\mathrm{3}}{\mathrm{16}} \\ $$

Question Number 158391 Answers: 2 Comments: 1

if α,β,γ are the angles of a triangle, find ((sin 2𝛂+sin 2𝛃+sin 2𝛄)/(sin 𝛂 sin 𝛃 sin 𝛄))=?

$${if}\:\alpha,\beta,\gamma\:{are}\:{the}\:{angles}\:{of}\:{a}\:{triangle}, \\ $$$${find}\:\frac{\boldsymbol{\mathrm{sin}}\:\mathrm{2}\boldsymbol{\alpha}+\boldsymbol{\mathrm{sin}}\:\mathrm{2}\boldsymbol{\beta}+\boldsymbol{\mathrm{sin}}\:\mathrm{2}\boldsymbol{\gamma}}{\boldsymbol{\mathrm{sin}}\:\boldsymbol{\alpha}\:\boldsymbol{\mathrm{sin}}\:\boldsymbol{\beta}\:\boldsymbol{\mathrm{sin}}\:\boldsymbol{\gamma}}=? \\ $$

Question Number 158383 Answers: 1 Comments: 0

Solve for real numbers: (1/(1 + tan^4 (x))) + (1/(10)) = (2/(1 + 3 tan^2 (x)))

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{tan}^{\mathrm{4}} \left(\boldsymbol{\mathrm{x}}\right)}\:+\:\frac{\mathrm{1}}{\mathrm{10}}\:=\:\frac{\mathrm{2}}{\mathrm{1}\:+\:\mathrm{3}\:\mathrm{tan}^{\mathrm{2}} \left(\boldsymbol{\mathrm{x}}\right)} \\ $$$$ \\ $$

Question Number 158379 Answers: 0 Comments: 1

F(x+1)−F(x−1)=6 F(0)=4 F(3)=?

$${F}\left({x}+\mathrm{1}\right)−{F}\left({x}−\mathrm{1}\right)=\mathrm{6} \\ $$$${F}\left(\mathrm{0}\right)=\mathrm{4} \\ $$$${F}\left(\mathrm{3}\right)=? \\ $$

Question Number 158378 Answers: 1 Comments: 0

How to graph order pair (3+5i , 4−2i)?

$${How}\:{to}\:{graph}\:{order}\:{pair}\:\left(\mathrm{3}+\mathrm{5}{i}\:,\:\mathrm{4}−\mathrm{2}{i}\right)? \\ $$

Question Number 158422 Answers: 2 Comments: 1

Question Number 158421 Answers: 2 Comments: 0

Question Number 158365 Answers: 0 Comments: 0

Question Number 158364 Answers: 0 Comments: 0

if a;b;c>0 prove that: a^(2a-(b+c)) ∙ b^(2b-(c+a)) ∙ c^(2c-(a+b)) ≥ 1

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\mathrm{a}^{\mathrm{2}\boldsymbol{\mathrm{a}}-\left(\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}\right)} \:\centerdot\:\mathrm{b}^{\mathrm{2}\boldsymbol{\mathrm{b}}-\left(\boldsymbol{\mathrm{c}}+\boldsymbol{\mathrm{a}}\right)} \:\centerdot\:\mathrm{c}^{\mathrm{2}\boldsymbol{\mathrm{c}}-\left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}\right)} \:\geqslant\:\mathrm{1} \\ $$$$ \\ $$

Question Number 158363 Answers: 1 Comments: 0

x;y;z>0 Solve for real numbers: { ((x^3 + y^3 + z^3 + 3∙((x)^(1/3) + (y)^(1/3) + (z)^(1/3) ) = 12)),((x∙y∙z = 1)) :}

$$\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0} \\ $$$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \:+\:\mathrm{3}\centerdot\left(\sqrt[{\mathrm{3}}]{\mathrm{x}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{y}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{z}}\right)\:=\:\mathrm{12}}\\{\mathrm{x}\centerdot\mathrm{y}\centerdot\mathrm{z}\:=\:\mathrm{1}}\end{cases} \\ $$$$ \\ $$

Question Number 158358 Answers: 0 Comments: 0

Question Number 158354 Answers: 0 Comments: 2

(√(sin ((π/4)+x))) +(√(sin ((π/4)−x))) =((2cos 2x))^(1/4)

$$\:\sqrt{\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}+{x}\right)}\:+\sqrt{\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}−{x}\right)}\:=\sqrt[{\mathrm{4}}]{\mathrm{2cos}\:\mathrm{2}{x}} \\ $$

Question Number 158341 Answers: 1 Comments: 0

Question Number 158340 Answers: 2 Comments: 0

1) Proven that by all n ∈ N^∗ 2!4!..(2n)!≥((n+1)!)^n 2) Proven by recurring that Σ_(p=1) ^n pp!=(n+1)!−1

$$\left.\mathrm{1}\right)\:{Proven}\:{that}\:{by}\:{all}\:{n}\:\in\:{N}^{\ast} \\ $$$$\:\mathrm{2}!\mathrm{4}!..\left(\mathrm{2}{n}\right)!\geqslant\left(\left({n}+\mathrm{1}\right)!\right)^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{Proven}\:{by}\:{recurring}\:{that}\: \\ $$$$\sum_{{p}=\mathrm{1}} ^{{n}} {pp}!=\left({n}+\mathrm{1}\right)!−\mathrm{1} \\ $$

Question Number 158334 Answers: 1 Comments: 3

lim_(x→∞) (1/x)Σ_(r=1) ^x cos(((rπ)/(2x))) x∈N

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{x}}\underset{{r}=\mathrm{1}} {\overset{{x}} {\sum}}{cos}\left(\frac{{r}\pi}{\mathrm{2}{x}}\right) \\ $$$${x}\in\mathbb{N} \\ $$

Question Number 158333 Answers: 0 Comments: 0

∫_((1;π)) ^((2;π)) (1−(y^2 /x^2 )cos((y/x)))dx+(sin((y/x))+(y/x)cos((y/x)))dy=? OY on the road that doesn′t cut your arrow

Question Number 158335 Answers: 2 Comments: 0

if α,β,γ are the angles of a triangle, find (1/(tan 𝛂 tan 𝛃))+(1/(tan 𝛃 tan 𝛄))+(1/(tan 𝛄 tan 𝛂))=?

$${if}\:\alpha,\beta,\gamma\:{are}\:{the}\:{angles}\:{of}\:{a}\:{triangle}, \\ $$$${find}\: \\ $$$$\frac{\mathrm{1}}{\boldsymbol{\mathrm{tan}}\:\boldsymbol{\alpha}\:\boldsymbol{\mathrm{tan}}\:\boldsymbol{\beta}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{tan}}\:\boldsymbol{\beta}\:\boldsymbol{\mathrm{tan}}\:\boldsymbol{\gamma}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{tan}}\:\boldsymbol{\gamma}\:\boldsymbol{\mathrm{tan}}\:\boldsymbol{\alpha}}=? \\ $$

Question Number 158331 Answers: 0 Comments: 0

Prove that: Σ_(n=1) ^∞ (1/( (√n) (n + 1))) < 2

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{n}}\:\left(\mathrm{n}\:+\:\mathrm{1}\right)}\:<\:\mathrm{2} \\ $$

Question Number 158330 Answers: 0 Comments: 1

Question Number 158327 Answers: 0 Comments: 0

Show that the sequence (x^n /(1 + x^n )) does not converge uniformly on [0, 2] by showing that the limit function is not continuous on [0, 2]

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sequence}\:\:\:\:\frac{\mathrm{x}^{\mathrm{n}} }{\mathrm{1}\:\:\:+\:\:\:\mathrm{x}^{\mathrm{n}} }\:\:\:\:\mathrm{does}\:\mathrm{not}\:\mathrm{converge}\:\mathrm{uniformly}\:\mathrm{on}\:\:\left[\mathrm{0},\:\:\mathrm{2}\right] \\ $$$$\mathrm{by}\:\mathrm{showing}\:\mathrm{that}\:\mathrm{the}\:\mathrm{limit}\:\mathrm{function}\:\mathrm{is}\:\mathrm{not}\:\mathrm{continuous}\:\mathrm{on}\:\:\:\:\left[\mathrm{0},\:\:\mathrm{2}\right] \\ $$

Question Number 158325 Answers: 2 Comments: 0

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