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AllQuestion and Answers: Page 551

Question Number 163618 Answers: 0 Comments: 0

Question Number 163613 Answers: 0 Comments: 0

Question Number 163614 Answers: 0 Comments: 0

∫((sec^2 x)/((secx+tanx)^(9/2) ))dx

$$\int\frac{{sec}^{\mathrm{2}} {x}}{\left({secx}+{tanx}\right)^{\mathrm{9}/\mathrm{2}} }{dx} \\ $$

Question Number 163611 Answers: 1 Comments: 0

Question Number 163610 Answers: 1 Comments: 0

Question Number 163609 Answers: 0 Comments: 0

lim_(n→∞) n[A−n(H_n −lnn−γ)]=B Find (A/B)=?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}n}\left[\mathrm{A}−\mathrm{n}\left(\mathrm{H}_{\mathrm{n}} −\mathrm{lnn}−\gamma\right)\right]=\mathrm{B} \\ $$$$\mathrm{Find}\:\frac{\mathrm{A}}{\mathrm{B}}=? \\ $$

Question Number 163608 Answers: 0 Comments: 0

A_n =(n/(n^2 +1^2 ))+(n/(n^2 +2^2 ))+...+(n/(n^2 +n^2 )) Prove:: lim_(n→∞) (1/(n^4 {(1/(24))−n[n((π/4)−A_n )−(1/4)]}))=2016

$$\mathrm{A}_{\mathrm{n}} =\frac{\mathrm{n}}{\mathrm{n}^{\mathrm{2}} +\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{n}}{\mathrm{n}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} }+...+\frac{\mathrm{n}}{\mathrm{n}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} } \\ $$$$\mathrm{Prove}::\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{4}} \left\{\frac{\mathrm{1}}{\mathrm{24}}−\mathrm{n}\left[\mathrm{n}\left(\frac{\pi}{\mathrm{4}}−\mathrm{A}_{\mathrm{n}} \right)−\frac{\mathrm{1}}{\mathrm{4}}\right]\right\}}=\mathrm{2016} \\ $$

Question Number 163601 Answers: 0 Comments: 0

∫_(2/π) ^(+oo) ln(cos((1/x)))dx narure?

$$\int_{\frac{\mathrm{2}}{\pi}} ^{+{oo}} {ln}\left({cos}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx} \\ $$$${narure}? \\ $$

Question Number 163600 Answers: 1 Comments: 0

a line charges of charge density pl=4x^3 −x+3mc/m laying along the x−axis. determine the total charge if the line charge extends from x=2 and x=6 m

$${a}\:{line}\:{charges}\:{of}\:{charge}\:{density}\: \\ $$$${pl}=\mathrm{4}{x}^{\mathrm{3}} −{x}+\mathrm{3}{mc}/{m}\:{laying}\:{along}\:{the}\:{x}−{axis}. \\ $$$${determine}\:{the}\:{total}\:{charge}\:{if}\:{the}\:{line}\:{charge} \\ $$$${extends}\:{from}\:{x}=\mathrm{2}\:{and}\:{x}=\mathrm{6}\:{m} \\ $$

Question Number 163591 Answers: 0 Comments: 3

Re^ soudre (∂^2 u/∂x^2 )+(∂^2 u/∂y^2 )=10e^(2x+y)

$$\mathrm{R}\acute {\mathrm{e}soudre}\:\:\:\:\:\:\frac{\partial^{\mathrm{2}} {u}}{\partial{x}^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} {u}}{\partial{y}^{\mathrm{2}} }=\mathrm{10}{e}^{\mathrm{2}{x}+{y}} \\ $$

Question Number 163586 Answers: 0 Comments: 0

Question Number 163587 Answers: 1 Comments: 0

Question Number 163588 Answers: 0 Comments: 0

In △ABC prove that (a/b) + (b/c) + (c/a) + (R^2 /(4r^2 )) ≥ 1 + (b^2 /a^2 ) + (c^2 /b^2 ) + (a^2 /c^2 )

$${In}\:\:\bigtriangleup{ABC}\:\:{prove}\:{that} \\ $$$$\frac{{a}}{{b}}\:+\:\frac{{b}}{{c}}\:+\:\frac{{c}}{{a}}\:+\:\frac{{R}^{\mathrm{2}} }{\mathrm{4}{r}^{\mathrm{2}} }\:\geqslant\:\mathrm{1}\:+\:\frac{{b}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\:+\:\frac{{c}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:+\:\frac{{a}^{\mathrm{2}} }{{c}^{\mathrm{2}} } \\ $$

Question Number 163582 Answers: 1 Comments: 0

lim_(x→∞) ((7^(x+2) +6^x )/(3^(2x) −5^x ))=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{7}^{{x}+\mathrm{2}} +\mathrm{6}^{{x}} }{\mathrm{3}^{\mathrm{2}{x}} −\mathrm{5}^{{x}} }=? \\ $$

Question Number 163770 Answers: 2 Comments: 0

solve : x,y ∈ N 3x + 5y = 20 −−−−−−−

$$ \\ $$$$\:\:\:\:\:{solve}\::\:\:\:\:{x},{y}\:\in\:\mathbb{N}\: \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{3}{x}\:+\:\mathrm{5}{y}\:=\:\mathrm{20}\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−−−−−−− \\ $$

Question Number 163769 Answers: 0 Comments: 0

lim_(x→∞) ((ln(1+((n!))^(1/n) ))/( (((2n−1)!!))^(1/n) ))=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{ln}\left(\mathrm{1}+\sqrt[{{n}}]{{n}!}\right)}{\:\sqrt[{{n}}]{\left(\mathrm{2}{n}−\mathrm{1}\right)!!}}=? \\ $$

Question Number 163767 Answers: 0 Comments: 0

Question Number 163580 Answers: 1 Comments: 1

∫ sin^(2021) (x) . sin(2023 x ) dx

$$\int\:{sin}^{\mathrm{2021}} \left({x}\right)\:.\:{sin}\left(\mathrm{2023}\:{x}\:\right)\:{dx}\: \\ $$

Question Number 163577 Answers: 0 Comments: 0

∫_(−1) ^( 1) ((1/(1−ax)))ln (((1+x)/(1−x))) dx

$$\:\:\:\int_{−\mathrm{1}} ^{\:\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{1}−\mathrm{ax}}\right)\mathrm{ln}\:\left(\frac{\mathrm{1}+\mathrm{x}}{\mathrm{1}−\mathrm{x}}\right)\:\mathrm{dx} \\ $$

Question Number 163576 Answers: 2 Comments: 0

What is the coefficient of x^(2020) in (1+x+x^2 +x^3 +...+x^(2020) )^(2021)

$$\:\:{What}\:{is}\:{the}\:{coefficient}\:{of}\:{x}^{\mathrm{2020}} \\ $$$$\:{in}\:\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +...+{x}^{\mathrm{2020}} \right)^{\mathrm{2021}} \\ $$

Question Number 163574 Answers: 1 Comments: 0

Show that; ∫_1 ^∞ ((In x)/x^4 ) dx = (1/9)

$$\boldsymbol{{Show}}\:\boldsymbol{{that}}; \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{1}} ^{\infty} \:\frac{\boldsymbol{{In}}\:\boldsymbol{{x}}}{\boldsymbol{{x}}^{\mathrm{4}} }\:\boldsymbol{{dx}}\:=\:\frac{\mathrm{1}}{\mathrm{9}} \\ $$

Question Number 163573 Answers: 0 Comments: 1

Question Number 163564 Answers: 0 Comments: 0

Find the closed form of a integral: 𝛀 = ∫_( (𝛑/2)) ^( 𝛑) (dx/(e^x + ln (cosx)))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{closed}\:\mathrm{form}\:\mathrm{of}\:\mathrm{a}\:\mathrm{integral}: \\ $$$$\boldsymbol{\Omega}\:\:=\:\underset{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\overset{\:\boldsymbol{\pi}} {\int}}\:\frac{\mathrm{dx}}{\mathrm{e}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{ln}\:\left(\mathrm{cos}\boldsymbol{\mathrm{x}}\right)} \\ $$

Question Number 163658 Answers: 2 Comments: 0

lim_(x→∞) ((sin (π/(2n))×sin ((2π)/(2n))×sin ((3π)/(2n))....×sin (((n−1)π)/n)))^(1/n) =?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt[{{n}}]{\mathrm{sin}\:\frac{\pi}{\mathrm{2}{n}}×\mathrm{sin}\:\frac{\mathrm{2}\pi}{\mathrm{2}{n}}×\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{2}{n}}....×\mathrm{sin}\:\frac{\left({n}−\mathrm{1}\right)\pi}{{n}}}=? \\ $$

Question Number 163657 Answers: 2 Comments: 0

lim_(x→0) (((1+x)^(1/x) −e)/x)=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{1}+{x}\right)^{\frac{\mathrm{1}}{{x}}} −{e}}{{x}}=? \\ $$

Question Number 163656 Answers: 1 Comments: 0

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