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Question Number 162860 Answers: 2 Comments: 0

Question Number 162859 Answers: 0 Comments: 0

Prove that: ∫_( 0) ^( (𝛑/2)) ((e^(cos 2x) ∙ sin(x + sin 2x))/(sin x)) dx = ((πe)/2)

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\int}}\:\frac{\mathrm{e}^{\boldsymbol{\mathrm{cos}}\:\mathrm{2}\boldsymbol{\mathrm{x}}} \:\centerdot\:\mathrm{sin}\left(\mathrm{x}\:+\:\mathrm{sin}\:\mathrm{2x}\right)}{\mathrm{sin}\:\mathrm{x}}\:\mathrm{dx}\:=\:\frac{\pi{e}}{\mathrm{2}} \\ $$

Question Number 162856 Answers: 0 Comments: 0

Question Number 162854 Answers: 0 Comments: 0

let a;b;c≥0 and a+b+c=3 prove that: ((a - 1)/( (√(b + 3)))) + ((b - 1)/( (√(c + 3)))) + ((c - 1)/( (√(a + 3)))) ≥ 0

$$\mathrm{let}\:\:\mathrm{a};\mathrm{b};\mathrm{c}\geqslant\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{3}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{a}\:-\:\mathrm{1}}{\:\sqrt{\mathrm{b}\:+\:\mathrm{3}}}\:+\:\frac{\mathrm{b}\:-\:\mathrm{1}}{\:\sqrt{\mathrm{c}\:+\:\mathrm{3}}}\:+\:\frac{\mathrm{c}\:-\:\mathrm{1}}{\:\sqrt{\mathrm{a}\:+\:\mathrm{3}}}\:\geqslant\:\mathrm{0} \\ $$

Question Number 162847 Answers: 2 Comments: 0

Question Number 162845 Answers: 1 Comments: 1

Question Number 162834 Answers: 5 Comments: 0

Question Number 162833 Answers: 1 Comments: 0

Question Number 162827 Answers: 1 Comments: 0

Question Number 162825 Answers: 2 Comments: 0

Question Number 162823 Answers: 2 Comments: 0

Given: x.p(x−1)=(x−5).p(x) and p(−1)=1. Find p((1/2)).

$$\:\:{Given}:\:\:{x}.{p}\left({x}−\mathrm{1}\right)=\left({x}−\mathrm{5}\right).{p}\left({x}\right) \\ $$$$\:\:{and}\:{p}\left(−\mathrm{1}\right)=\mathrm{1}.\: \\ $$$$\:\:{Find}\:{p}\left(\frac{\mathrm{1}}{\mathrm{2}}\right). \\ $$

Question Number 163727 Answers: 0 Comments: 0

Question Number 163724 Answers: 0 Comments: 0

Question Number 162819 Answers: 0 Comments: 1

#combinatorial mathematics# In how many subsets of 10 members of the set , { 1, 2, ..., 20 } is there no difference between two members of 5 ? a: 2^( 10) b : 3^( 5) c : 2^( 8) d: 10^( 4)

$$ \\ $$$$\:\:\:\:\:#{combinatorial}\:{mathematics}# \\ $$$$\:\:\:\:\:\:\mathrm{I}{n}\:{how}\:{many}\:\:{subsets}\:{of}\:\mathrm{10}\: \\ $$$${members}\:{of}\:\:{the}\:{set}\:,\:\left\{\:\mathrm{1},\:\mathrm{2},\:...,\:\mathrm{20}\:\right\} \\ $$$$\:\:\:{is}\:{there}\:{no}\:{difference}\:{between} \\ $$$$\:{two}\:{members}\:{of}\:\:\:\:\mathrm{5}\:?\: \\ $$$${a}:\:\:\mathrm{2}^{\:\mathrm{10}} \:\:\:\:\:\:{b}\::\:\:\mathrm{3}^{\:\mathrm{5}} \:\:\:\:\:\:\:{c}\::\:\:\:\mathrm{2}^{\:\mathrm{8}} \:\:\:\:\:\:\:\:{d}:\:\:\:\mathrm{10}^{\:\mathrm{4}} \\ $$

Question Number 162814 Answers: 2 Comments: 0

Question Number 162811 Answers: 1 Comments: 0

I = ∫_0 ^( ∞) (( tan^( −1) (x ))/(( 1+x^( 2) )^( 2) )) dx = ? −−−−−−−−−−

$$ \\ $$$$\:\:\:\:\:\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{tan}^{\:−\mathrm{1}} \:\left({x}\:\right)}{\left(\:\mathrm{1}+{x}^{\:\mathrm{2}} \:\right)^{\:\mathrm{2}} }\:{dx}\:=\:? \\ $$$$\:\:\:\:\:\:−−−−−−−−−− \\ $$

Question Number 162809 Answers: 2 Comments: 0

if y = x + (1/(x+(1/(x+(1/x)._._._._. )))) find y^′

$${if}\:{y}\:=\:{x}\:+\:\frac{\mathrm{1}}{{x}+\frac{\mathrm{1}}{{x}+\frac{\mathrm{1}}{{x}}._{._{._{._{.} } } } }}\:\:{find}\:{y}^{'} \\ $$

Question Number 162804 Answers: 2 Comments: 0

Ω = ∫ sin^( 2) (x).cos^( 4) (x ) dx

$$ \\ $$$$ \\ $$$$\:\:\:\Omega\:=\:\int\:{sin}^{\:\mathrm{2}} \left({x}\right).{cos}^{\:\mathrm{4}} \left({x}\:\right)\:{dx} \\ $$$$ \\ $$

Question Number 162794 Answers: 0 Comments: 0

Question Number 162792 Answers: 1 Comments: 0

Find: 𝛀 = ∫_( 0) ^( ∞) ((arctan(x))/(x∙(x^2 - x + 1))) dx

$$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:\:=\:\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{arctan}\left(\mathrm{x}\right)}{\mathrm{x}\centerdot\left(\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{x}\:+\:\mathrm{1}\right)}\:\mathrm{dx} \\ $$

Question Number 162791 Answers: 3 Comments: 0

Question Number 162790 Answers: 1 Comments: 0

Calculate lim_(n→∞) (1+2^n +3^n )^(1/n)

$${Calculate}\: \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\mathrm{2}^{{n}} +\mathrm{3}^{{n}} \right)^{\frac{\mathrm{1}}{{n}}} \\ $$

Question Number 162788 Answers: 1 Comments: 0

let x;y;z > 0 such that x^4 +y^4 +z^4 = x^2 +y^2 +z^2 find the minimum of the expression: P = (x^2 /y) + (y^2 /z) + (z^2 /x)

$$\mathrm{let}\:\:\mathrm{x};\mathrm{y};\mathrm{z}\:>\:\mathrm{0} \\ $$$$\mathrm{such}\:\mathrm{that}\:\:\mathrm{x}^{\mathrm{4}} +\mathrm{y}^{\mathrm{4}} +\mathrm{z}^{\mathrm{4}} \:=\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expression}: \\ $$$$\mathrm{P}\:=\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{y}}\:+\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{z}}\:+\:\frac{\mathrm{z}^{\mathrm{2}} }{\mathrm{x}} \\ $$

Question Number 162787 Answers: 1 Comments: 0

happy new year {a;b;c}∈Z−{0} p(x)=ax^2 +bx+c p(a)=0 p(b)=0 p(1)=?

$$\boldsymbol{\mathrm{happy}}\:\boldsymbol{\mathrm{new}}\:\boldsymbol{\mathrm{year}} \\ $$$$\left\{\boldsymbol{{a}};\boldsymbol{{b}};\boldsymbol{{c}}\right\}\in\mathbb{Z}−\left\{\mathrm{0}\right\} \\ $$$$\boldsymbol{{p}}\left(\boldsymbol{{x}}\right)=\boldsymbol{{ax}}^{\mathrm{2}} +\boldsymbol{{bx}}+\boldsymbol{{c}}\:\:\:\: \\ $$$$\boldsymbol{{p}}\left(\boldsymbol{{a}}\right)=\mathrm{0} \\ $$$$\boldsymbol{{p}}\left(\boldsymbol{{b}}\right)=\mathrm{0} \\ $$$$\boldsymbol{{p}}\left(\mathrm{1}\right)=? \\ $$

Question Number 162783 Answers: 0 Comments: 0

Question Number 162782 Answers: 0 Comments: 0

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