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Question Number 48172    Answers: 0   Comments: 1

calculate ∫_0 ^∞ ((sin(2cos(x^2 +1)))/(1+x^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{sin}\left(\mathrm{2}{cos}\left({x}^{\mathrm{2}} +\mathrm{1}\right)\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 48171    Answers: 0   Comments: 1

calculate ∫_0 ^∞ ((sin(cosx))/(x^2 +3))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{sin}\left({cosx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$

Question Number 48170    Answers: 1   Comments: 1

calculate ∫_0 ^∞ ((cos(sin(x^2 )))/(1+2x^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({sin}\left({x}^{\mathrm{2}} \right)\right)}{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 48165    Answers: 0   Comments: 0

In a version of millikan experiment it is a charged droplet of mass 1.8x10^(−15) kg just remain stationary where the p.d between the plates which are 12mm apart is 150v. If the droplet suddenly gain an extra electron. Find (a) the acceleration of the droplet (b) the p.d to bring it back to stationary possition. PLEASE HELP

$$\mathrm{In}\:\mathrm{a}\:\mathrm{version}\:\mathrm{of}\:\mathrm{millikan}\:\mathrm{experiment}\:\mathrm{it}\:\mathrm{is} \\ $$$$\mathrm{a}\:\mathrm{charged}\:\mathrm{droplet}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{1}.\mathrm{8x10}^{−\mathrm{15}} \mathrm{kg} \\ $$$$\mathrm{just}\:\mathrm{remain}\:\mathrm{stationary}\:\mathrm{where}\:\mathrm{the}\:\mathrm{p}.\mathrm{d}\: \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{plates}\:\mathrm{which}\:\mathrm{are}\:\mathrm{12mm} \\ $$$$\mathrm{apart}\:\mathrm{is}\:\mathrm{150v}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{droplet}\:\mathrm{suddenly} \\ $$$$\mathrm{gain}\:\mathrm{an}\:\mathrm{extra}\:\mathrm{electron}.\:\mathrm{Find} \\ $$$$\:\:\:\left(\mathrm{a}\right)\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{droplet} \\ $$$$\:\:\:\left(\mathrm{b}\right)\:\mathrm{the}\:\mathrm{p}.\mathrm{d}\:\mathrm{to}\:\mathrm{bring}\:\mathrm{it}\:\mathrm{back}\:\mathrm{to}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{stationary}\:\mathrm{possition}. \\ $$$$\boldsymbol{\mathrm{P}}\mathrm{LEASE}\:\mathrm{HELP} \\ $$

Question Number 48169    Answers: 0   Comments: 1

let u_n =∫_0 ^∞ cos(nx^2 )dx and v_n =∫_0 ^∞ sin(nx^2 )dx with n >0 1) calculste u_n and v_n 2)find nsture of Σ(u_n +2v_n ) and Σ (u_n ^2 +4v_n ^2 ) 3)find nature of Σ(u_n +2v_n )^2

$${let}\:{u}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{cos}\left({nx}^{\mathrm{2}} \right){dx}\:{and}\:{v}_{{n}} =\int_{\mathrm{0}} ^{\infty} {sin}\left({nx}^{\mathrm{2}} \right){dx}\:{with}\:{n}\:>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculste}\:{u}_{{n}} {and}\:{v}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{nsture}\:{of}\:\Sigma\left({u}_{{n}} +\mathrm{2}{v}_{{n}} \right)\:{and}\:\Sigma\:\left({u}_{{n}} ^{\mathrm{2}} \:+\mathrm{4}{v}_{{n}} ^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{3}\right){find}\:{nature}\:{of}\:\Sigma\left({u}_{{n}} +\mathrm{2}{v}_{{n}} \right)^{\mathrm{2}} \\ $$$$ \\ $$

Question Number 48161    Answers: 1   Comments: 1

f(z)=((1−z)/(1+z)) u(x,y)=.. v(x,y)=..

$${f}\left({z}\right)=\frac{\mathrm{1}−{z}}{\mathrm{1}+{z}} \\ $$$${u}\left({x},{y}\right)=.. \\ $$$${v}\left({x},{y}\right)=.. \\ $$$$ \\ $$$$ \\ $$

Question Number 48156    Answers: 2   Comments: 1

Question Number 48155    Answers: 1   Comments: 0

((√2))^x =((√3))^y x≠0 y ≠ 0 find x,y

$$\left(\sqrt{\mathrm{2}}\right)^{{x}} =\left(\sqrt{\mathrm{3}}\right)^{{y}} \\ $$$${x}\neq\mathrm{0} \\ $$$${y}\:\neq\:\mathrm{0} \\ $$$$\mathrm{find}\:{x},{y} \\ $$

Question Number 48143    Answers: 1   Comments: 1

The locus of P(x,y) such that (√(x^2 +y^2 +8y+16))−(√(x^2 +y^2 −6x+9))=5 is?

$${The}\:{locus}\:{of}\:{P}\left({x},{y}\right)\:{such}\:{that} \\ $$$$\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{8}{y}+\mathrm{16}}−\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{9}}=\mathrm{5}\:{is}? \\ $$

Question Number 48129    Answers: 1   Comments: 0

how we can show _3_(√2) on axis?

$$\mathrm{how}\:\mathrm{we}\:\mathrm{can}\:\mathrm{show}\:\:\:_{\mathrm{3}_{\sqrt{\mathrm{2}}} } \:\:\mathrm{on}\:\mathrm{axis}? \\ $$

Question Number 48127    Answers: 1   Comments: 0

Question Number 48121    Answers: 0   Comments: 3

can the directrix of a parabola be in the form y=mx+b ? or is there an inclined parabola with directrix and axis of symmetry in the form of y=mx+b ??

$${can}\:{the}\:{directrix}\:{of}\:{a}\:{parabola}\:{be}\:{in}\:{the}\:{form}\:{y}={mx}+{b}\:\:? \\ $$$${or}\:{is}\:{there}\:{an}\:{inclined}\:{parabola}\:{with}\:{directrix}\:{and}\:{axis}\: \\ $$$${of}\:{symmetry}\:{in}\:{the}\:{form}\:{of}\:{y}={mx}+{b}\:\:?? \\ $$

Question Number 48118    Answers: 0   Comments: 0

(√(a^2 x^2 −y^2 ))+(√(b^2 x^2 −y^2 )) = (a+b)(√(2x^2 +(x^4 /(x^4 −y^2 )))) Find x such that y is minimum. Assume x, y > 0 .

$$\sqrt{{a}^{\mathrm{2}} {x}^{\mathrm{2}} −{y}^{\mathrm{2}} }+\sqrt{{b}^{\mathrm{2}} {x}^{\mathrm{2}} −{y}^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\left({a}+{b}\right)\sqrt{\mathrm{2}{x}^{\mathrm{2}} +\frac{{x}^{\mathrm{4}} }{{x}^{\mathrm{4}} −{y}^{\mathrm{2}} }} \\ $$$${Find}\:{x}\:{such}\:{that}\:{y}\:{is}\:{minimum}. \\ $$$$\:\:{Assume}\:\:\:{x},\:{y}\:>\:\mathrm{0}\:. \\ $$

Question Number 48117    Answers: 0   Comments: 0

thanks sir

$${thanks}\:{sir} \\ $$

Question Number 48113    Answers: 2   Comments: 0

Question Number 48111    Answers: 1   Comments: 0

(−46−×)/(−2)=60 hi sir plx help me

$$\left(−\mathrm{46}−×\right)/\left(−\mathrm{2}\right)=\mathrm{60}\:\: \\ $$$${hi}\:{sir}\:{plx}\:{help}\:{me} \\ $$

Question Number 48105    Answers: 1   Comments: 2

∫_(−1) ^1 ((√(1+x+x^2 ))− (√(1−x−x^2 )) )dx =

$$\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\:\left(\sqrt{\mathrm{1}+{x}+{x}^{\mathrm{2}} }−\:\sqrt{\mathrm{1}−{x}−{x}^{\mathrm{2}} }\:\right){dx}\:= \\ $$

Question Number 48104    Answers: 1   Comments: 0

solve this ∫(2 sinx+cosx)/(2+3sinx+sin^(2x) ) dx

$$\mathrm{solve}\:\mathrm{this}\:\: \\ $$$$\int\left(\mathrm{2}\:\mathrm{sinx}+\mathrm{cosx}\right)/\left(\mathrm{2}+\mathrm{3sinx}+\mathrm{sin}^{\mathrm{2x}} \right)\:\mathrm{dx} \\ $$

Question Number 48103    Answers: 0   Comments: 0

6

$$\mathrm{6} \\ $$

Question Number 48091    Answers: 1   Comments: 2

Question Number 48090    Answers: 1   Comments: 0

Question Number 48078    Answers: 1   Comments: 0

Question Number 48075    Answers: 1   Comments: 1

solve (∣x^2 −1∣−(1/2))x+((√6)/(18))=0

$$\mathrm{solve}\:\:\:\:\:\left(\mid{x}^{\mathrm{2}} −\mathrm{1}\mid−\frac{\mathrm{1}}{\mathrm{2}}\right){x}+\frac{\sqrt{\mathrm{6}}}{\mathrm{18}}=\mathrm{0} \\ $$

Question Number 48068    Answers: 1   Comments: 1

let u_n =∫_0 ^∞ (dt/(1+t^n )) find nature of Σ u_n and Σ (u_n /n^2 ) and Σ (u_n /n^3 )

$${let}\:{u}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dt}}{\mathrm{1}+{t}^{{n}} } \\ $$$${find}\:{nature}\:{of}\:\Sigma\:{u}_{{n}} \:\:\:\:{and}\:\Sigma\:\frac{{u}_{{n}} }{{n}^{\mathrm{2}} }\:\:{and}\:\Sigma\:\frac{{u}_{{n}} }{{n}^{\mathrm{3}} } \\ $$

Question Number 48067    Answers: 0   Comments: 1

let y>0 give ∫_0 ^∞ (x^y /(e^x −1))dx at form of series.

$${let}\:{y}>\mathrm{0}\:{give}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{{y}} }{{e}^{{x}} −\mathrm{1}}{dx}\:{at}\:{form}\:{of}\:{series}. \\ $$

Question Number 48066    Answers: 1   Comments: 4

(√(1/2)).(√((1/2)+(1/2)(√(1/2)))).(√((1/2)+(1/2)(√((1/2)+(1/2)(√(1/2))))))......∞=?

$$\sqrt{\frac{\mathrm{1}}{\mathrm{2}}}.\sqrt{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\frac{\mathrm{1}}{\mathrm{2}}}}.\sqrt{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\frac{\mathrm{1}}{\mathrm{2}}}}}......\infty=? \\ $$

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