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Question Number 204815 Answers: 2 Comments: 0

Given (3p^2 −p+q^3 )^(12) , find the coefficient of p^(10) q^6

$$\:\:\:\:\:\mathrm{Given}\:\left(\mathrm{3p}^{\mathrm{2}} −\mathrm{p}+\mathrm{q}^{\mathrm{3}} \right)^{\mathrm{12}} \:,\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\:\:\:\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{p}^{\mathrm{10}} \mathrm{q}^{\mathrm{6}} \\ $$

Question Number 204805 Answers: 0 Comments: 5

Why lim_(n→∞) (x^n u_n )=0 ,When u_n is bounded

$$\mathrm{Why}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left({x}^{{n}} {u}_{{n}} \right)=\mathrm{0}\:,\mathrm{When}\:{u}_{{n}} \:\mathrm{is}\:\mathrm{bounded}\: \\ $$

Question Number 204804 Answers: 1 Comments: 3

Evaluate ∫((sinx)/(x^4 +x^2 +1))dx I need full detailed explanation, thank you in advance.

$$\mathrm{Evaluate}\:\int\frac{\mathrm{sinx}}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{dx} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{I}\:\mathrm{need}\:\mathrm{full}\:\mathrm{detailed}\:\mathrm{explanation},\:\mathrm{thank}\:\mathrm{you}\:\mathrm{in} \\ $$$$\mathrm{advance}. \\ $$

Question Number 204802 Answers: 1 Comments: 0

Wi-Fi code problem: ∫_(−2) ^( 2) (x^3 cos((x/2))+(1/2))(√(4−x^2 ))dx

$$\mathrm{Wi}-\mathrm{Fi}\:\mathrm{code}\:\mathrm{problem}: \\ $$$$\int_{−\mathrm{2}} ^{\:\mathrm{2}} \left({x}^{\mathrm{3}} \mathrm{cos}\left(\frac{{x}}{\mathrm{2}}\right)+\frac{\mathrm{1}}{\mathrm{2}}\right)\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }\mathrm{d}{x} \\ $$

Question Number 204800 Answers: 1 Comments: 0

Question Number 204783 Answers: 0 Comments: 0

Question Number 204756 Answers: 1 Comments: 23

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Question Number 204754 Answers: 1 Comments: 0

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Question Number 204739 Answers: 2 Comments: 0

Question Number 204742 Answers: 1 Comments: 4

Solve for real x

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:{x} \\ $$

Question Number 204733 Answers: 2 Comments: 0

Find: ((59^2 + 48^2 + 41^2 − 30^2 )/(68^2 + 52^2 + 32^2 − 48^2 )) = ?

$$\mathrm{Find}:\:\:\:\frac{\mathrm{59}^{\mathrm{2}} \:+\:\mathrm{48}^{\mathrm{2}} \:+\:\mathrm{41}^{\mathrm{2}} \:−\:\mathrm{30}^{\mathrm{2}} }{\mathrm{68}^{\mathrm{2}} \:+\:\mathrm{52}^{\mathrm{2}} \:+\:\mathrm{32}^{\mathrm{2}} \:−\:\mathrm{48}^{\mathrm{2}} }\:=\:? \\ $$

Question Number 204729 Answers: 1 Comments: 0

Question Number 204753 Answers: 0 Comments: 7

A wave has an amplitude of 20cm from rest. If the angle of oscillation is 30⁰. Find the displacement of the wave.

Question Number 204715 Answers: 2 Comments: 0

prove that ∫_0 ^1 ((ln^2 (1−x))/x)dx=2ζ(3)

$${prove}\:{that} \\ $$$$\overset{\mathrm{1}} {\int}_{\mathrm{0}} \frac{{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}\right)}{{x}}{dx}=\mathrm{2}\zeta\left(\mathrm{3}\right) \\ $$$$ \\ $$

Question Number 204712 Answers: 5 Comments: 1

Find all real solution (√(3x^2 +x−1)) +(√(x^2 −2x−3)) = (√(3x^2 +3x+5)) + (√(x^2 +3))

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{real}\:\mathrm{solution}\: \\ $$$$\:\:\:\:\sqrt{\mathrm{3x}^{\mathrm{2}} +\mathrm{x}−\mathrm{1}}\:+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}−\mathrm{3}}\:=\: \\ $$$$\:\:\sqrt{\mathrm{3x}^{\mathrm{2}} +\mathrm{3x}+\mathrm{5}}\:+\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{3}}\: \\ $$

Question Number 204707 Answers: 1 Comments: 0

integrate ∫_0 ^∞ (e^(−x^2 ) /(1+e^x ))dx

$$\boldsymbol{{integrate}}\:\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{{e}}^{−\boldsymbol{{x}}^{\mathrm{2}} } }{\mathrm{1}+\boldsymbol{{e}}^{\boldsymbol{{x}}} }\boldsymbol{{dx}} \\ $$

Question Number 204706 Answers: 0 Comments: 0

evaluate ∫_0 ^∞ 2^(−𝚪(x)) dx

$$\boldsymbol{{evaluate}}\:\int_{\mathrm{0}} ^{\infty} \mathrm{2}^{−\boldsymbol{\Gamma}\left(\boldsymbol{{x}}\right)} \boldsymbol{{dx}} \\ $$

Question Number 204705 Answers: 0 Comments: 1

evalute ∫_0 ^∞ 2^(−(√(tanx))) dx

$$\boldsymbol{{evalute}}\:\int_{\mathrm{0}} ^{\infty} \mathrm{2}^{−\sqrt{\boldsymbol{{tanx}}}} \boldsymbol{{dx}} \\ $$

Question Number 204702 Answers: 1 Comments: 0

prove that : cl(Q×Q )=^? R^2 note: (X ,d ) is a metric space , A ⊆ X : x∈ A^( −) =cl(A) ⇔ ∀ r >0 , B_r (x) ∩ A ≠ φ

$$ \\ $$$$\:\:\:\mathrm{prove}\:\mathrm{that}\:: \\ $$$$\:\:\:\:\:\:\:\mathrm{cl}\left(\mathbb{Q}×\mathbb{Q}\:\right)\overset{?} {=}\:\mathbb{R}^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:{note}:\:\:\:\left({X}\:,{d}\:\right)\:{is}\:{a}\:{metric}\:{space} \\ $$$$\:\:\:\:\:\:\:\:\:\:,\:\:\:{A}\:\subseteq\:{X}\::\:\:\:\:\:{x}\in\:\overset{\:\:−} {{A}}=\mathrm{cl}\left({A}\right)\:\Leftrightarrow\:\forall\:{r}\:>\mathrm{0}\:,\:{B}_{{r}} \:\left({x}\right)\:\cap\:{A}\:\neq\:\phi \\ $$

Question Number 204701 Answers: 3 Comments: 0

Question Number 204717 Answers: 1 Comments: 0

((3^0 +3^1 +3^2 +.........+ 3^(200) )/(13)) =^(Remainder) ?

$$\frac{\mathrm{3}^{\mathrm{0}} +\mathrm{3}^{\mathrm{1}} +\mathrm{3}^{\mathrm{2}} \:+.........+\:\mathrm{3}^{\mathrm{200}} }{\mathrm{13}}\:\overset{\mathrm{Remainder}} {=}\:? \\ $$

Question Number 204691 Answers: 1 Comments: 0

(√(a÷(√(a÷(√(a÷∙∙∙÷(√a)))))))=?

$$\sqrt{{a}\boldsymbol{\div}\sqrt{{a}\boldsymbol{\div}\sqrt{{a}\boldsymbol{\div}\centerdot\centerdot\centerdot\boldsymbol{\div}\sqrt{{a}}}}}=? \\ $$

Question Number 204690 Answers: 1 Comments: 0

((a^x ÷((b^y ÷(c^z )^(1/r) ))^(1/q) ))^(1/p) =?

$$\sqrt[{{p}}]{{a}^{{x}} \boldsymbol{\div}\sqrt[{{q}}]{{b}^{{y}} \boldsymbol{\div}\sqrt[{{r}}]{{c}^{{z}} }}}=? \\ $$

Question Number 204689 Answers: 1 Comments: 0

y=∣f(x)∣ ; (dy/dx)=?

$${y}=\mid{f}\left({x}\right)\mid\:\:;\:\:\:\:\frac{{dy}}{{dx}}=? \\ $$

Question Number 204688 Answers: 1 Comments: 0

f(x)=sgn(x); f^′ (x)=(d/dx)[f(x)]=?

$${f}\left({x}\right)={sgn}\left({x}\right);\:\:\:\:\:{f}^{'} \left({x}\right)=\frac{{d}}{{dx}}\left[{f}\left({x}\right)\right]=? \\ $$

Question Number 204687 Answers: 0 Comments: 0

(√(a−(√(b−(√c)))))=?

$$\sqrt{{a}−\sqrt{{b}−\sqrt{{c}}}}=? \\ $$

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