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Question Number 183693    Answers: 1   Comments: 0

lim_(x→+∞) (((ln x)^x )/x^(ln x) )

$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\frac{\left(\mathrm{ln}\:{x}\right)^{{x}} }{{x}^{\mathrm{ln}\:{x}} } \\ $$

Question Number 183690    Answers: 1   Comments: 0

Question Number 183687    Answers: 3   Comments: 0

∫(1/(lnx))dx Help out

$$\int\frac{\mathrm{1}}{\mathrm{lnx}}\mathrm{dx} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}\:\mathrm{out} \\ $$

Question Number 183678    Answers: 0   Comments: 0

find the laplace invesrse for I(s) I(s)=((2000s^2 )/((s^2 +200^2 )(s^2 +400s+2×10^5 )))

$${find}\:{the}\:{laplace}\:{invesrse}\:{for}\:{I}\left({s}\right) \\ $$$${I}\left({s}\right)=\frac{\mathrm{2000}{s}^{\mathrm{2}} }{\left({s}^{\mathrm{2}} +\mathrm{200}^{\mathrm{2}} \right)\left({s}^{\mathrm{2}} +\mathrm{400}{s}+\mathrm{2}×\mathrm{10}^{\mathrm{5}} \right)} \\ $$

Question Number 183673    Answers: 1   Comments: 0

lim_(x→0) [sin^2 ((𝛑/(2−ax)))]^(sec^2 ((𝛑/(2−bx))))

$$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\boldsymbol{\mathrm{lim}}}\:\:\left[\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \left(\frac{\boldsymbol{\pi}}{\mathrm{2}−\boldsymbol{{a}\mathrm{x}}}\right)\right]^{\boldsymbol{\mathrm{sec}}^{\mathrm{2}} \left(\frac{\boldsymbol{\pi}}{\mathrm{2}−\boldsymbol{\mathrm{bx}}}\right)} \\ $$

Question Number 183669    Answers: 4   Comments: 0

f(x)= (x/(1 + x + x^( 2) )) min_( f) = ?

$$ \\ $$$$\:\:\:\:\:{f}\left({x}\right)=\:\frac{{x}}{\mathrm{1}\:+\:{x}\:+\:{x}^{\:\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:{min}_{\:{f}} \:=\:? \\ $$

Question Number 183668    Answers: 1   Comments: 1

x , y , z ∈R: If { (((1/x) +(1/(y+z)) =(1/2))),(((1/y) +(1/(x+z)) = (1/3))),(((1/z_ ) +(1/(x+y)) =(1/4))) :} ⇒ x , y , z =?

$$ \\ $$$$\:\:\:\:\:\:{x}\:,\:{y}\:,\:{z}\:\in\mathbb{R}: \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\mathrm{If}\:\:\:\:\begin{cases}{\frac{\mathrm{1}}{{x}}\:+\frac{\mathrm{1}}{{y}+{z}}\:=\frac{\mathrm{1}}{\mathrm{2}}}\\{\frac{\mathrm{1}}{{y}}\:+\frac{\mathrm{1}}{{x}+{z}}\:=\:\frac{\mathrm{1}}{\mathrm{3}}}\\{\frac{\mathrm{1}}{{z}_{\:} }\:+\frac{\mathrm{1}}{{x}+{y}}\:=\frac{\mathrm{1}}{\mathrm{4}}}\end{cases} \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\:\:\:{x}\:,\:{y}\:,\:{z}\:=? \\ $$$$ \\ $$

Question Number 183667    Answers: 0   Comments: 8

If w is one of the complex cube roots of unity, show that (a+wb+w^2 c)(a+w^2 b+wc) is equal to (α^2 +b^2 +c^2 −ab−bc−cα). Kindly help me out, Thank you.

$$\mathrm{If}\:\mathrm{w}\:\mathrm{is}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{cube}\: \\ $$$$\mathrm{roots}\:\mathrm{of}\:\mathrm{unity},\:\mathrm{show}\:\mathrm{that} \\ $$$$\left(\mathrm{a}+\mathrm{wb}+\mathrm{w}^{\mathrm{2}} \mathrm{c}\right)\left(\mathrm{a}+\mathrm{w}^{\mathrm{2}} \mathrm{b}+\mathrm{wc}\right)\:\mathrm{is}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\left(\alpha^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} −\mathrm{ab}−\mathrm{bc}−\mathrm{c}\alpha\right). \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Kindly}\:\mathrm{help}\:\mathrm{me}\:\mathrm{out},\:\mathrm{Thank}\:\mathrm{you}. \\ $$

Question Number 183664    Answers: 0   Comments: 4

How many artificially made weights are required (minimally) to weigh ONLY 1,3,5,...,79 kg and what should be they?

$$ \\ $$$$\mathcal{H}{ow}\:{many}\:{artificially}\:{made}\:{weights}\:{are}\: \\ $$$$\boldsymbol{{required}}\:\left({minimally}\right)\:{to}\:{weigh} \\ $$$$\:\underline{\mathrm{ONLY}}\:\:\:\:\:\mathrm{1},\mathrm{3},\mathrm{5},...,\mathrm{79}\:{kg}\: \\ $$$${and}\:{what}\:{should}\:{be}\:{they}? \\ $$

Question Number 183663    Answers: 2   Comments: 1

Question Number 183660    Answers: 3   Comments: 0

what is larger, 2022^(2022) or 2021^(2023) ?

$${what}\:{is}\:{larger}, \\ $$$$\mathrm{2022}^{\mathrm{2022}} \:{or}\:\mathrm{2021}^{\mathrm{2023}} \:? \\ $$

Question Number 183646    Answers: 0   Comments: 4

How many artificially made weights are required (minimally) to weigh 1,3,5,...,79 kg and what should be they?

$$\mathcal{H}{ow}\:{many}\:{artificially}\:{made}\:{weights}\:{are}\: \\ $$$$\boldsymbol{{required}}\:\left({minimally}\right)\:{to}\:{weigh} \\ $$$$\:\mathrm{1},\mathrm{3},\mathrm{5},...,\mathrm{79}\:{kg}\: \\ $$$${and}\:{what}\:{should}\:{be}\:{they}? \\ $$

Question Number 183644    Answers: 4   Comments: 1

Question Number 183638    Answers: 0   Comments: 0

find y(t) y(t)+2e^t ∫_0 ^t (y(τ)−e^(−τ) )dτ=te^t

$${find}\:{y}\left({t}\right) \\ $$$${y}\left({t}\right)+\mathrm{2}{e}^{{t}} \int_{\mathrm{0}} ^{{t}} \left({y}\left(\tau\right)−{e}^{−\tau} \right){d}\tau={te}^{{t}} \\ $$

Question Number 183628    Answers: 1   Comments: 2

surface du rectangle?

$${surface}\:{du}\:{rectangle}? \\ $$

Question Number 183620    Answers: 1   Comments: 1

determiner l aire du triangle CDE

$${determiner}\:{l}\:{aire}\:\:{du}\:{triangle}\:{CDE} \\ $$

Question Number 183617    Answers: 0   Comments: 3

How many artificially made weights are required (minimally) to weigh 2,4,6,...,80 kg and what should be they?

$$\mathcal{H}{ow}\:{many}\:{artificially}\:{made}\:{weights}\:{are}\: \\ $$$$\boldsymbol{{required}}\:\left({minimally}\right)\:{to}\:{weigh} \\ $$$$\:\mathrm{2},\mathrm{4},\mathrm{6},...,\mathrm{80}\:{kg}\: \\ $$$${and}\:{what}\:{should}\:{be}\:{they}? \\ $$

Question Number 183600    Answers: 1   Comments: 3

y′^(′′) + 8y′^(′′) +12y′ = 0 Solve with better explanation

$$\mathrm{y}'^{''} \:+\:\mathrm{8y}'^{''} \:+\mathrm{12y}'\:=\:\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Solve}\:\mathrm{with}\:\mathrm{better}\:\mathrm{explanation} \\ $$

Question Number 183583    Answers: 1   Comments: 1

Question Number 183563    Answers: 1   Comments: 1

repost an unsolved question Q182552 Find the period of the following: a• sin 4x sin 3x b• sin πx+ cos x c• ((2 sin^2 3x− 3 tan 4x+ 4 cot 6x)/(∣cosec 8x∣− sec^3 10x+ (√(cot 12x))))

$$\mathrm{repost}\:\mathrm{an}\:\mathrm{unsolved}\:\mathrm{question}\:\mathrm{Q182552} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{period}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}: \\ $$$$\:{a}\bullet\:\mathrm{sin}\:\mathrm{4}{x}\:\mathrm{sin}\:\mathrm{3}{x} \\ $$$$\:{b}\bullet\:\mathrm{sin}\:\pi{x}+\:\mathrm{cos}\:{x} \\ $$$$\:{c}\bullet\:\frac{\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{3}{x}−\:\mathrm{3}\:\mathrm{tan}\:\mathrm{4}{x}+\:\mathrm{4}\:\mathrm{cot}\:\mathrm{6}{x}}{\mid\mathrm{cosec}\:\mathrm{8}{x}\mid−\:\mathrm{sec}^{\mathrm{3}} \:\mathrm{10}{x}+\:\sqrt{\mathrm{cot}\:\mathrm{12}{x}}} \\ $$

Question Number 183559    Answers: 1   Comments: 0

∫_1 ^∞ (dx/(x^2 +(√x))) = ?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{\mathrm{1}} {\overset{\infty} {\int}}\:\frac{{dx}}{{x}^{\mathrm{2}} +\sqrt{{x}}}\:=\:?\: \\ $$

Question Number 183558    Answers: 3   Comments: 1

Question Number 183556    Answers: 1   Comments: 0

Question Number 183551    Answers: 1   Comments: 0

Question Number 183536    Answers: 1   Comments: 1

radius of convergence of serie: Σ_(nεN) ((cos(((3π)/3)))/5^n )z^n

$${radius}\:{of}\:{convergence}\:{of}\:{serie}: \\ $$$$\underset{{n}\epsilon{N}} {\sum}\frac{{cos}\left(\frac{\mathrm{3}\pi}{\mathrm{3}}\right)}{\mathrm{5}^{{n}} }{z}^{{n}} \\ $$

Question Number 183535    Answers: 2   Comments: 0

Who is greater? 70^(71) or 71^(70)

$${Who}\:{is}\:{greater}?\:\mathrm{70}^{\mathrm{71}} \:{or}\:\:\mathrm{71}^{\mathrm{70}} \\ $$

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