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Question Number 166764 Answers: 1 Comments: 0

(dy/dx)=cos(y−x)

$$\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}=\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{y}}−\boldsymbol{\mathrm{x}}\right)\:\: \\ $$

Question Number 166759 Answers: 0 Comments: 0

Question Number 166756 Answers: 2 Comments: 0

Evaluate: ∫_0 ^( ∞) (((x + 1)^(2020) )/((x + 2)^(2022) )) dx = ?

$$\mathrm{Evaluate}: \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\frac{\left(\mathrm{x}\:+\:\mathrm{1}\right)^{\mathrm{2020}} }{\left(\mathrm{x}\:+\:\mathrm{2}\right)^{\mathrm{2022}} }\:\mathrm{dx}\:=\:? \\ $$

Question Number 166754 Answers: 1 Comments: 0

Question Number 166749 Answers: 1 Comments: 1

Question Number 166738 Answers: 3 Comments: 1

Question Number 166737 Answers: 0 Comments: 2

Today i came across a question, and im somehow confuse about it... The question was.... Show that 4+2=6 indicating all the properties and operations on real numbers.

$${Today}\:{i}\:{came}\:{across}\:{a}\:{question}, \\ $$$${and}\:{im}\:{somehow}\:{confuse}\:{about}\:{it}... \\ $$$$\:{The}\:{question}\:{was}.... \\ $$$$\:{Show}\:{that}\:\mathrm{4}+\mathrm{2}=\mathrm{6} \\ $$$$\:{indicating}\:{all}\:{the}\:{properties}\:{and} \\ $$$${operations}\:{on}\:{real}\:{numbers}. \\ $$

Question Number 166735 Answers: 0 Comments: 0

For some constant α∈(0,1) calculate: ∫_0 ^∞ e^(−(t^α /α)−xt) dt∼(√((2π)/(1−α)))∙x^(−(α/(2(1−α)))−1) e^(((1−α)/α)∙x^(−(α/(1−α))) ) ,x→0^+

$$\mathrm{For}\:\:\mathrm{some}\:\mathrm{constant}\:\alpha\in\left(\mathrm{0},\mathrm{1}\right) \\ $$$$\mathrm{calculate}:\:\:\:\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\frac{\mathrm{t}^{\alpha} }{\alpha}−\mathrm{xt}} \mathrm{dt}\sim\sqrt{\frac{\mathrm{2}\pi}{\mathrm{1}−\alpha}}\centerdot\mathrm{x}^{−\frac{\alpha}{\mathrm{2}\left(\mathrm{1}−\alpha\right)}−\mathrm{1}} \mathrm{e}^{\frac{\mathrm{1}−\alpha}{\alpha}\centerdot\mathrm{x}^{−\frac{\alpha}{\mathrm{1}−\alpha}} } ,\mathrm{x}\rightarrow\mathrm{0}^{+} \\ $$

Question Number 166725 Answers: 2 Comments: 2

∫ (dx/(3+tan x))=?

$$\:\:\:\int\:\frac{\mathrm{dx}}{\mathrm{3}+\mathrm{tan}\:\mathrm{x}}=? \\ $$

Question Number 166723 Answers: 1 Comments: 0

∫ (((x)^(1/5) −1)/( (√x) + 1)) dx=?

$$\:\:\:\int\:\frac{\sqrt[{\mathrm{5}}]{\mathrm{x}}\:−\mathrm{1}}{\:\sqrt{\mathrm{x}}\:+\:\mathrm{1}}\:\mathrm{dx}=? \\ $$

Question Number 166719 Answers: 0 Comments: 1

sin xcos xcos 2x=a any price to a is corect the answer a=?

$$\mathrm{sin}\:{x}\mathrm{cos}\:{x}\mathrm{cos}\:\mathrm{2}{x}={a} \\ $$$${any}\:{price}\:{to}\:{a} \\ $$$${is}\:{corect}\:{the}\:{answer}\:\:\:\:{a}=? \\ $$

Question Number 166718 Answers: 0 Comments: 1

csc10−(√3)sec10=?

$${csc}\mathrm{10}−\sqrt{\mathrm{3}}{sec}\mathrm{10}=? \\ $$

Question Number 166715 Answers: 1 Comments: 0

The perimeter of an equilateral triangle is 24. Find it′s area.

$$\mathrm{The}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{an}\:\mathrm{equilateral} \\ $$$$\mathrm{triangle}\:\mathrm{is}\:\mathrm{24}.\:\mathrm{Find}\:\mathrm{it}'\mathrm{s}\:\mathrm{area}. \\ $$

Question Number 166707 Answers: 1 Comments: 0

(8/(1×5×9))+(8/(5×9×13))+(8/(9×13×17))+…+(1/(41×45×49))=? by M.A

$$\frac{\mathrm{8}}{\mathrm{1}×\mathrm{5}×\mathrm{9}}+\frac{\mathrm{8}}{\mathrm{5}×\mathrm{9}×\mathrm{13}}+\frac{\mathrm{8}}{\mathrm{9}×\mathrm{13}×\mathrm{17}}+\ldots+\frac{\mathrm{1}}{\mathrm{41}×\mathrm{45}×\mathrm{49}}=? \\ $$$$ \\ $$$$ \\ $$$$\boldsymbol{{by}}\:\boldsymbol{{M}}.\boldsymbol{{A}} \\ $$

Question Number 166702 Answers: 0 Comments: 1

∫e^x ln(x)dx=..???

$$\int{e}^{{x}} {ln}\left({x}\right){dx}=..??? \\ $$

Question Number 166701 Answers: 2 Comments: 0

Question Number 166699 Answers: 1 Comments: 0

lim_(n→∞) Σ_(k=n) ^(2n) sin (π/k)=?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{n}} {\overset{\mathrm{2n}} {\sum}}\mathrm{sin}\:\frac{\pi}{\mathrm{k}}=? \\ $$

Question Number 166697 Answers: 0 Comments: 1

Σ_(n=0) ^∞ (1/((3n)!)) =^? (1/3) [e + ((2cos((3/( 2(√3)))))/( (√e)))]

$$\:\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\left(\mathrm{3n}\right)!}\:\overset{?} {=}\:\frac{\mathrm{1}}{\mathrm{3}}\:\left[\mathrm{e}\:+\:\frac{\mathrm{2cos}\left(\frac{\mathrm{3}}{\:\mathrm{2}\sqrt{\mathrm{3}}}\right)}{\:\sqrt{\mathrm{e}}}\right] \\ $$$$\: \\ $$

Question Number 166690 Answers: 1 Comments: 0

Calculate If , 𝛗= ∫_0 ^( 1) (( tanh^( −1) ( x^( 3) ))/x) dx = α.ζ( 2) then , α = ? ■ M.N −−−−−−−

$$ \\ $$$$\:\:\:\:\:\:\:\:\:{Calculate}\: \\ $$$$\:\:\:\:\:{If}\:\:,\:\boldsymbol{\phi}=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{tanh}^{\:−\mathrm{1}} \left(\:{x}^{\:\mathrm{3}} \:\right)}{{x}}\:{dx}\:=\:\alpha.\zeta\left(\:\mathrm{2}\right)\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{then}\:,\:\:\:\:\:\alpha\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\blacksquare\:\mathscr{M}.\mathscr{N}\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−−−−−−− \\ $$$$ \\ $$

Question Number 166687 Answers: 1 Comments: 1

log _((2x−1)) (x+1) > log _((4−2x)) (x+1) x=?

$$\:\:\:\mathrm{log}\:_{\left(\mathrm{2x}−\mathrm{1}\right)} \left(\mathrm{x}+\mathrm{1}\right)\:>\:\mathrm{log}\:_{\left(\mathrm{4}−\mathrm{2x}\right)} \left(\mathrm{x}+\mathrm{1}\right) \\ $$$$\:\:\mathrm{x}=? \\ $$

Question Number 166686 Answers: 0 Comments: 1

Question Number 166685 Answers: 0 Comments: 0

sec^2 1°+sec^2 2°+sec^2 3°+...+sec^2 89°=?

$$\:\:\:\mathrm{sec}\:^{\mathrm{2}} \mathrm{1}°+\mathrm{sec}\:^{\mathrm{2}} \mathrm{2}°+\mathrm{sec}\:^{\mathrm{2}} \mathrm{3}°+...+\mathrm{sec}\:^{\mathrm{2}} \mathrm{89}°=? \\ $$

Question Number 166684 Answers: 0 Comments: 0

T = ∫ ((sin (x^2 +2))/(2x+4)) dx=?

$$\:\:\:\:\:\:\mathrm{T}\:=\:\int\:\frac{\mathrm{sin}\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2}\right)}{\mathrm{2x}+\mathrm{4}}\:\mathrm{dx}=? \\ $$

Question Number 166683 Answers: 0 Comments: 0

Question Number 166678 Answers: 1 Comments: 0

4+x+2x=8+2(3+x)−3 Find x

$$\mathrm{4}+\boldsymbol{{x}}+\mathrm{2}\boldsymbol{{x}}=\mathrm{8}+\mathrm{2}\left(\mathrm{3}+\boldsymbol{{x}}\right)−\mathrm{3} \\ $$$$\boldsymbol{{F}}{ind}\:{x} \\ $$$$ \\ $$

Question Number 166676 Answers: 1 Comments: 0

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