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Question Number 14486 Answers: 0 Comments: 0

S=1−2+3−4+... ∴S=Σ_(n=1) ^∞ (−1)^(n+1) n S=lim_(s→0) (Σ_(n=1) ^∞ (−1)^(n+1) n^(1−s) ) Prove S=(1/4)

$${S}=\mathrm{1}−\mathrm{2}+\mathrm{3}−\mathrm{4}+... \\ $$$$\therefore{S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} {n} \\ $$$$\: \\ $$$${S}=\underset{{s}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} {n}^{\mathrm{1}−{s}} \right) \\ $$$$\: \\ $$$$\mathrm{Prove}\:{S}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 14483 Answers: 0 Comments: 8

x^y +y^x =3.....(1) x+y=3.....(2) solve the equation

$$\mathrm{x}^{\mathrm{y}} +\mathrm{y}^{\mathrm{x}} =\mathrm{3}.....\left(\mathrm{1}\right) \\ $$$$\mathrm{x}+\mathrm{y}=\mathrm{3}.....\left(\mathrm{2}\right) \\ $$$$ \\ $$$$\mathrm{solve}\:\mathrm{the}\:\mathrm{equation} \\ $$

Question Number 14481 Answers: 0 Comments: 0

Question Number 14479 Answers: 1 Comments: 0

Question Number 14478 Answers: 2 Comments: 0

Solve: y′ = (y − x)^2

$$\mathrm{Solve}:\:\:\:\:\mathrm{y}'\:=\:\left(\mathrm{y}\:−\:\mathrm{x}\right)^{\mathrm{2}} \\ $$

Question Number 14470 Answers: 0 Comments: 4

Find the number of solution(s) of x^2 + x + sin x = 0, x ∈ [0, π]

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solution}\left(\mathrm{s}\right)\:\mathrm{of} \\ $$$${x}^{\mathrm{2}} \:+\:{x}\:+\:\mathrm{sin}\:{x}\:=\:\mathrm{0},\:{x}\:\in\:\left[\mathrm{0},\:\pi\right] \\ $$

Question Number 14468 Answers: 0 Comments: 0

Question Number 14467 Answers: 0 Comments: 6

Question Number 14452 Answers: 1 Comments: 3

Question Number 14451 Answers: 2 Comments: 0

Question Number 14444 Answers: 1 Comments: 0

Solve the differential equation y′ = ((2x + 3y − 4)/(4x + 3y + 2))

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}\: \\ $$$$\mathrm{y}'\:=\:\frac{\mathrm{2x}\:+\:\mathrm{3y}\:−\:\mathrm{4}}{\mathrm{4x}\:+\:\mathrm{3y}\:+\:\mathrm{2}} \\ $$

Question Number 14440 Answers: 1 Comments: 0

Question Number 14438 Answers: 1 Comments: 3

x=((2a)/(√3))sin 𝛉, y=((2b)/(√3))sin 𝛗, and z=((2c)/(√3))sin 𝛙 ; where a,b, and c are sides of △ABC such that 𝛗−𝛙+(π/3)=∠A, 𝛙−𝛉+(π/3)=∠B, and 𝛉−𝛙+(π/3)=∠C . Find at least one feasible solution set of 𝛉,𝛗, and 𝛙 in terms of ∠A, ∠B, and ∠C such that all angles and sides are positive with a≠b≠c , and ∠A≠∠B≠∠C ≠ (𝛑/2) Find x,y, and z even if you you please..

$$\boldsymbol{{x}}=\frac{\mathrm{2}\boldsymbol{{a}}}{\sqrt{\mathrm{3}}}\mathrm{sin}\:\boldsymbol{\theta},\:\boldsymbol{{y}}=\frac{\mathrm{2}\boldsymbol{{b}}}{\sqrt{\mathrm{3}}}\mathrm{sin}\:\boldsymbol{\phi},\:{and} \\ $$$$\boldsymbol{{z}}=\frac{\mathrm{2}\boldsymbol{{c}}}{\sqrt{\mathrm{3}}}\mathrm{sin}\:\boldsymbol{\psi}\:;\:{where}\:\boldsymbol{{a}},\boldsymbol{{b}},\:{and}\:\boldsymbol{{c}} \\ $$$${are}\:{sides}\:{of}\:\bigtriangleup{ABC}\:{such}\:{that} \\ $$$$\boldsymbol{\phi}−\boldsymbol{\psi}+\frac{\pi}{\mathrm{3}}=\angle\boldsymbol{{A}}, \\ $$$$\boldsymbol{\psi}−\boldsymbol{\theta}+\frac{\pi}{\mathrm{3}}=\angle\boldsymbol{{B}},\:{and} \\ $$$$\boldsymbol{\theta}−\boldsymbol{\psi}+\frac{\pi}{\mathrm{3}}=\angle\boldsymbol{{C}}\:. \\ $$$${Find}\:{at}\:{least}\:{one}\:{feasible} \\ $$$${solution}\:{set}\:{of}\:\boldsymbol{\theta},\boldsymbol{\phi},\:{and}\:\boldsymbol{\psi}\:{in} \\ $$$${terms}\:{of}\:\angle\boldsymbol{{A}},\:\angle\boldsymbol{{B}},\:{and}\:\angle\boldsymbol{{C}} \\ $$$${such}\:{that}\:{all}\:{angles}\:{and}\:{sides} \\ $$$${are}\:{positive}\:{with}\:\boldsymbol{{a}}\neq\boldsymbol{{b}}\neq\boldsymbol{{c}}\:, \\ $$$${and}\:\angle\boldsymbol{{A}}\neq\angle\boldsymbol{{B}}\neq\angle\boldsymbol{{C}}\:\:\neq\:\frac{\boldsymbol{\pi}}{\mathrm{2}}\: \\ $$$${Find}\:\boldsymbol{{x}},\boldsymbol{{y}},\:{and}\:\boldsymbol{{z}}\:{even}\:{if}\:{you}\: \\ $$$${you}\:{please}.. \\ $$

Question Number 14435 Answers: 0 Comments: 0

∫e^(−x^2 ) dx=?

$$\int{e}^{−{x}^{\mathrm{2}} } {dx}=? \\ $$

Question Number 14431 Answers: 0 Comments: 0

∫ ((3x sin^(−1) (4x^2 ))/(√(1 − 16x^4 ))) dx

$$\int\:\:\frac{\mathrm{3x}\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{4x}^{\mathrm{2}} \right)}{\sqrt{\mathrm{1}\:−\:\mathrm{16x}^{\mathrm{4}} }}\:\mathrm{dx} \\ $$

Question Number 14430 Answers: 0 Comments: 0

y = (x^2 + y^4 )^2 , find (dy/dx) with respect to x

$$\mathrm{y}\:=\:\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{4}} \right)^{\mathrm{2}} \:,\:\:\mathrm{find}\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to}\:\mathrm{x} \\ $$

Question Number 14421 Answers: 1 Comments: 0

express ((2x^2 −x+2)/((x+2)^2 (1−2x)))as partial fraction