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Question Number 186868 Answers: 2 Comments: 1

Question Number 186867 Answers: 2 Comments: 0

Question Number 186863 Answers: 0 Comments: 0

Question Number 186864 Answers: 2 Comments: 0

if AB,BA and BB three tow digits natural numbers if (((AB+BA))/(BB))=4 then find the maximum volue of (A+B)=?

$${if}\:\:{AB},{BA}\:{and}\:{BB}\:\:{three}\:\:{tow}\:{digits}\:{natural} \\ $$$${numbers}\:{if}\:\:\frac{\left({AB}+{BA}\right)}{{BB}}=\mathrm{4} \\ $$$${then}\:{find}\:{the}\:{maximum}\:{volue}\:{of} \\ $$$$\left({A}+{B}\right)=? \\ $$

Question Number 193967 Answers: 1 Comments: 0

Question Number 186858 Answers: 0 Comments: 0

Discuss according to the value of the parametre α∈R the convergence of the improper integral ∫_0 ^(+∞) x^α ln(x+e^(αx) )dx

$${Discuss}\:{according}\:{to}\:{the}\:{value}\:{of}\:{the}\:{parametre} \\ $$$$\alpha\in\mathbb{R}\:{the}\:{convergence}\:{of}\:{the}\:{improper}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{+\infty} {x}^{\alpha} {ln}\left({x}+{e}^{\alpha{x}} \right){dx} \\ $$

Question Number 186856 Answers: 0 Comments: 0

∫ (((√(x+3))+(√(x+2)))/( (√(x+3))+(√(x−2)))) dx =?

$$\int\:\frac{\sqrt{{x}+\mathrm{3}}+\sqrt{{x}+\mathrm{2}}}{\:\sqrt{{x}+\mathrm{3}}+\sqrt{{x}−\mathrm{2}}}\:{dx}\:=? \\ $$

Question Number 186854 Answers: 1 Comments: 0

∫_0 ^( R) ((Rcosx)/(l−Rcosx))dx=?

$$\int_{\mathrm{0}} ^{\:{R}} \frac{{Rcosx}}{{l}−{Rcosx}}{dx}=? \\ $$

Question Number 186853 Answers: 1 Comments: 0

lim(k→∞)Σ_(i=1) ^k (1/( (√(ki))))=?

$${lim}\left({k}\rightarrow\infty\right)\underset{{i}=\mathrm{1}} {\overset{{k}} {\sum}}\frac{\mathrm{1}}{\:\sqrt{{ki}}}=? \\ $$

Question Number 186849 Answers: 0 Comments: 1

Question Number 186841 Answers: 0 Comments: 0

Question Number 186840 Answers: 1 Comments: 0

∫_9 ^( 16) ((√(4−(√x)))/x) dx =?

$$\:\:\underset{\mathrm{9}} {\overset{\:\mathrm{16}} {\int}}\:\frac{\sqrt{\mathrm{4}−\sqrt{{x}}}}{{x}}\:{dx}\:=? \\ $$

Question Number 186838 Answers: 3 Comments: 0

Question Number 186837 Answers: 0 Comments: 0

Question Number 186835 Answers: 0 Comments: 1

Question Number 186833 Answers: 1 Comments: 1

Question Number 186830 Answers: 1 Comments: 1

Question Number 186821 Answers: 1 Comments: 0

Question Number 188822 Answers: 1 Comments: 3

is it a polynomial? p(x)=2x^2 +4x^x −10

$${is}\:{it}\:{a}\:{polynomial}? \\ $$$${p}\left({x}\right)=\mathrm{2}{x}^{\mathrm{2}} +\mathrm{4}{x}^{{x}} −\mathrm{10} \\ $$

Question Number 186809 Answers: 1 Comments: 0

Question Number 186808 Answers: 0 Comments: 0

Question Number 186805 Answers: 1 Comments: 0

Question Number 186803 Answers: 1 Comments: 0

Question Number 186800 Answers: 0 Comments: 0

show that ∫_0 ^( ∞ ) ((tan^(−1) 𝛂x tan^(−1) 𝛃x)/x^2 )dx = (𝛑/2)log{(((𝛂+𝛃)^(𝛂+𝛃) )/(𝛂^𝛂 𝛃^𝛃 ))}

$$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{\mathrm{0}} ^{\:\infty\:} \frac{\boldsymbol{\mathrm{tan}}^{−\mathrm{1}} \boldsymbol{\alpha{x}}\:\boldsymbol{\mathrm{tan}}^{−\mathrm{1}} \boldsymbol{\beta{x}}}{\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}\:=\:\frac{\boldsymbol{\pi}}{\mathrm{2}}\mathrm{log}\left\{\frac{\left(\boldsymbol{\alpha}+\boldsymbol{\beta}\right)^{\boldsymbol{\alpha}+\boldsymbol{\beta}} }{\boldsymbol{\alpha}^{\boldsymbol{\alpha}} \boldsymbol{\beta}^{\boldsymbol{\beta}} }\right\}\: \\ $$

Question Number 186790 Answers: 0 Comments: 0

Solve using Fourier′s series: x^2 (1−x)y′′−x(1+x)y′+y=0

$${Solve}\:{using}\:{Fourier}'{s}\:{series}: \\ $$$${x}^{\mathrm{2}} \left(\mathrm{1}−{x}\right){y}''−{x}\left(\mathrm{1}+{x}\right){y}'+{y}=\mathrm{0} \\ $$

Question Number 186788 Answers: 1 Comments: 0

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