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Question Number 103481    Answers: 1   Comments: 0

prove that (cos((nθ)/5)+isin((2nθ)/(10)))^5 −(1/e^(inθ) )=2sin(nθ) ?

$${prove}\:{that}\:\left({cos}\frac{{n}\theta}{\mathrm{5}}+{isin}\frac{\mathrm{2}{n}\theta}{\mathrm{10}}\right)^{\mathrm{5}} −\frac{\mathrm{1}}{{e}^{{in}\theta} }=\mathrm{2}{sin}\left({n}\theta\right)\:? \\ $$

Question Number 103480    Answers: 0   Comments: 0

if f(x)=∣x−1 0<x<1∣ solve in (1)Fourier series of sines only ? (2) Fourier series of cosines ?

$${if}\:{f}\left({x}\right)=\mid{x}−\mathrm{1}\:\:\:\:\:\:\mathrm{0}<{x}<\mathrm{1}\mid\:{solve}\:{in} \\ $$$$ \\ $$$$\left(\mathrm{1}\right){Fourier}\:{series}\:{of}\:{sines}\:{only}\:? \\ $$$$\left(\mathrm{2}\right)\:{Fourier}\:{series}\:{of}\:{cosines}\:? \\ $$

Question Number 103479    Answers: 1   Comments: 0

by ussing laplace find cosh(2t)cos(4t) ?

$${by}\:{ussing}\:{laplace}\:{find}\:{cosh}\left(\mathrm{2}{t}\right){cos}\left(\mathrm{4}{t}\right)\:? \\ $$

Question Number 103478    Answers: 4   Comments: 0

Question Number 103477    Answers: 0   Comments: 0

Question Number 103468    Answers: 2   Comments: 0

(d^2 y/dx^2 ) + 2 (dy/dx) +2y = cos 4x? by UC method

$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{2}\:\frac{{dy}}{{dx}}\:+\mathrm{2}{y}\:=\:\mathrm{cos}\:\mathrm{4}{x}? \\ $$$${by}\:{UC}\:{method}\: \\ $$

Question Number 103463    Answers: 2   Comments: 0

lim_(x→∞) ((ln(3e^(2x) +5e^x −2))/(ln(27e^(3x) −1))) ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{ln}\left(\mathrm{3}{e}^{\mathrm{2}{x}} +\mathrm{5}{e}^{{x}} −\mathrm{2}\right)}{\mathrm{ln}\left(\mathrm{27}{e}^{\mathrm{3}{x}} −\mathrm{1}\right)}\:? \\ $$

Question Number 103459    Answers: 2   Comments: 6

what are the complex solution tan (z) = −2 ?

$${what}\:{are}\:{the}\:{complex}\:{solution}\:\mathrm{tan} \\ $$$$\left({z}\right)\:=\:−\mathrm{2}\:? \\ $$

Question Number 103458    Answers: 2   Comments: 0

(1)If p and q are the roots quadratic equation x^2 −x−4050 = 0 , find the value of p^2 +q ? (2) if f(x)=((7x+q)/2) and g(x)=7x+8 ; (fog)(4) = 24 . find the value of q

$$\left(\mathrm{1}\right){If}\:{p}\:{and}\:{q}\:{are}\:{the}\:{roots}\:{quadratic} \\ $$$${equation}\:{x}^{\mathrm{2}} −{x}−\mathrm{4050}\:=\:\mathrm{0}\:,\:{find}\:{the}\:{value} \\ $$$${of}\:{p}^{\mathrm{2}} +{q}\:?\: \\ $$$$\left(\mathrm{2}\right)\:{if}\:{f}\left({x}\right)=\frac{\mathrm{7}{x}+{q}}{\mathrm{2}}\:{and}\:{g}\left({x}\right)=\mathrm{7}{x}+\mathrm{8}\:; \\ $$$$\left({fog}\right)\left(\mathrm{4}\right)\:=\:\mathrm{24}\:.\:{find}\:{the}\:{value}\:{of}\:{q} \\ $$

Question Number 103457    Answers: 2   Comments: 0

f(((1−x)/(1+x))) = x+2 then what is the domain and range of f^(−1) (x) ?

$${f}\left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)\:=\:{x}+\mathrm{2}\:{then}\:{what}\:{is}\:{the}\:{domain} \\ $$$${and}\:{range}\:{of}\:{f}^{−\mathrm{1}} \left({x}\right)\:? \\ $$

Question Number 103454    Answers: 1   Comments: 0

∫ (x^2 +2x^4 +3x^6 )(√(1+x^2 +x^4 )) dx

$$\int\:\left({x}^{\mathrm{2}} +\mathrm{2}{x}^{\mathrm{4}} +\mathrm{3}{x}^{\mathrm{6}} \right)\sqrt{\mathrm{1}+{x}^{\mathrm{2}} +{x}^{\mathrm{4}} }\:{dx}\: \\ $$

Question Number 103449    Answers: 1   Comments: 0

Question Number 103448    Answers: 1   Comments: 0

Question Number 103436    Answers: 2   Comments: 0

Π_(n = 3) ^∞ (1−(4/n^2 )) = ?

$$\underset{\mathrm{n}\:=\:\mathrm{3}} {\overset{\infty} {\prod}}\left(\mathrm{1}−\frac{\mathrm{4}}{\mathrm{n}^{\mathrm{2}} }\right)\:=\:? \\ $$

Question Number 103450    Answers: 1   Comments: 0

Question Number 103422    Answers: 0   Comments: 2

Question Number 103421    Answers: 1   Comments: 0

Question Number 103419    Answers: 1   Comments: 0

Question Number 103412    Answers: 1   Comments: 0

solve (1+x^2 )^2 y^(′′) +2x(1+x^2 )y^′ +2=0

$${solve}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} {y}^{''} \:+\mathrm{2}{x}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{'} \:+\mathrm{2}=\mathrm{0} \\ $$

Question Number 103411    Answers: 2   Comments: 0

solve x^2 y^(′′) +xy^′ +y =0

$${solve}\:{x}^{\mathrm{2}} {y}^{''} \:+{xy}^{'} \:+{y}\:=\mathrm{0} \\ $$

Question Number 103410    Answers: 1   Comments: 0

Σ_(k=0) ^n (((−1)^k )/(k!))=?

$$\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{k}} }{\mathrm{k}!}=? \\ $$

Question Number 103409    Answers: 0   Comments: 1

What will be the state of a system(isolated)when its entropy tends to zero or zero? Time get stopped?? or another things may happen I am thinking about this

$$\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{state}\:\mathrm{of}\:\mathrm{a}\:\mathrm{system}\left(\mathrm{isolated}\right)\mathrm{when}\:\mathrm{its}\:\mathrm{entropy}\:\mathrm{tends} \\ $$$$\mathrm{to}\:\mathrm{zero}\:\mathrm{or}\:\mathrm{zero}? \\ $$$$ \\ $$$$\mathrm{T}\boldsymbol{\mathrm{ime}}\:\boldsymbol{\mathrm{get}}\:\boldsymbol{\mathrm{stopped}}?? \\ $$$$\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{another}}\:\boldsymbol{\mathrm{things}}\:\boldsymbol{\mathrm{may}}\:\boldsymbol{\mathrm{happen}} \\ $$$$\boldsymbol{\mathrm{I}}\:\boldsymbol{\mathrm{am}}\:\boldsymbol{\mathrm{thinking}}\:\boldsymbol{\mathrm{about}}\:\boldsymbol{\mathrm{this}} \\ $$

Question Number 103406    Answers: 0   Comments: 3

100 students are standing in a row. 4 students should be selected in the way that no two of them are next to each other. how many ways do you have to do this?

$$\mathrm{100}\:{students}\:{are}\:{standing}\:{in}\:{a}\:{row}. \\ $$$$\mathrm{4}\:{students}\:{should}\:{be}\:{selected}\:{in}\:{the} \\ $$$${way}\:{that}\:{no}\:{two}\:{of}\:{them}\:{are}\:{next}\:{to} \\ $$$${each}\:{other}.\:{how}\:{many}\:{ways}\:{do}\:{you} \\ $$$${have}\:{to}\:{do}\:{this}? \\ $$

Question Number 103400    Answers: 3   Comments: 1

A particle′s trajectory is described by x=e^t +e^(−t) y=2t Find the distance that the particle traveled for 0≤t≤2

$$\mathrm{A}\:\mathrm{particle}'\mathrm{s}\:\mathrm{trajectory}\:\mathrm{is}\:\mathrm{described}\:\mathrm{by} \\ $$$$\mathrm{x}=\mathrm{e}^{\mathrm{t}} +\mathrm{e}^{−\mathrm{t}} \:\:\:\:\:\mathrm{y}=\mathrm{2t} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{that}\:\mathrm{the}\:\mathrm{particle} \\ $$$$\mathrm{traveled}\:\mathrm{for}\:\mathrm{0}\leqslant\mathrm{t}\leqslant\mathrm{2} \\ $$

Question Number 103397    Answers: 1   Comments: 0

I(n)=∫_0 ^∞ ((ln x)/(cosh^n x ))dx is there a simpler way to calculat those values

$${I}\left({n}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\:{x}}{\mathrm{cosh}^{{n}} {x}\:}{dx} \\ $$$${is}\:{there}\:{a}\:{simpler}\:{way}\:{to} \\ $$$${calculat}\:{those}\:{values} \\ $$

Question Number 103393    Answers: 2   Comments: 0

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