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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))))))......∞=?

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

Question Number 48065    Answers: 0   Comments: 1

let f : ]0,1[ contnue integrable u_n =(−1)^n ∫_0 ^1 x^n f(x)dx prove that Σ u_n cnverge and find its sum

$$\left.{let}\:{f}\:\:\:\::\:\:\right]\mathrm{0},\mathrm{1}\left[\:\:{contnue}\:{integrable}\:\:{u}_{{n}} =\left(−\mathrm{1}\right)^{{n}} \:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} {f}\left({x}\right){dx}\right. \\ $$$${prove}\:{that}\:\Sigma\:{u}_{{n}} \:{cnverge}\:{and}\:{find}\:{its}\:{sum} \\ $$$$ \\ $$

Question Number 48064    Answers: 1   Comments: 1

calculate A =∫_0 ^1 (1+x^2 )(√(1−x^2 ))dx −∫_0 ^1 (1−x^2 )(√(1+x^2 ))dx

$${calculate}\:{A}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }{dx}\:\:−\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 48063    Answers: 0   Comments: 0

let W(x) =∫_(−∞) ^(+∞) ((arctan(xt^2 ))/(2+t^2 ))dt 1) find a explicit form of f(x) 2) find the value of ∫_(−∞) ^(+∞) (t^2 /((2+t^2 )(1+x^2 t^4 )))dt .

$${let}\:{W}\left({x}\right)\:=\int_{−\infty} ^{+\infty} \:\:\frac{{arctan}\left({xt}^{\mathrm{2}} \right)}{\mathrm{2}+{t}^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{t}^{\mathrm{2}} }{\left(\mathrm{2}+{t}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{2}} {t}^{\mathrm{4}} \right)}{dt}\:. \\ $$

Question Number 48062    Answers: 0   Comments: 0

calculate ∫_(−∞) ^(+∞) (((x^2 −3)sin(2x^2 ))/((x^2 +1)^3 ))dx

$${calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{\left({x}^{\mathrm{2}} −\mathrm{3}\right){sin}\left(\mathrm{2}{x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }{dx} \\ $$

Question Number 48057    Answers: 2   Comments: 1

Question Number 48052    Answers: 2   Comments: 1

Question Number 48050    Answers: 1   Comments: 1

Question Number 48055    Answers: 2   Comments: 6

Solve the system: { ((x^3 +x^2 y−4xy^2 −4y^3 =0)),((x^2 −2xy−3y^2 −x−y=0)) :}

$${Solve}\:{the}\:{system}: \\ $$$$\begin{cases}{{x}^{\mathrm{3}} +{x}^{\mathrm{2}} {y}−\mathrm{4}{xy}^{\mathrm{2}} −\mathrm{4}{y}^{\mathrm{3}} =\mathrm{0}}\\{{x}^{\mathrm{2}} −\mathrm{2}{xy}−\mathrm{3}{y}^{\mathrm{2}} −{x}−{y}=\mathrm{0}}\end{cases} \\ $$

Question Number 48043    Answers: 0   Comments: 1

let f(α) =∫_(−∞) ^(+∞) ((cos(αx^3 ))/(x^2 +8)) dx 1)calculate f(α) 2) calculate ∫_(−∞) ^(+∞) ((cos(2x^3 ))/(x^2 +8))dx .

$${let}\:{f}\left(\alpha\right)\:=\int_{−\infty} ^{+\infty} \:\:\frac{{cos}\left(\alpha{x}^{\mathrm{3}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{8}}\:{dx} \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}\left(\alpha\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{cos}\left(\mathrm{2}{x}^{\mathrm{3}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{8}}{dx}\:. \\ $$

Question Number 48042    Answers: 0   Comments: 1

find the value of ∫_(−∞) ^(+∞) ((2x+1)/((x^2 +i)(x^2 +4)))dx (i^2 =−1)

$${find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{\mathrm{2}{x}+\mathrm{1}}{\left({x}^{\mathrm{2}} +{i}\right)\left({x}^{\mathrm{2}} +\mathrm{4}\right)}{dx}\:\:\:\left({i}^{\mathrm{2}} =−\mathrm{1}\right) \\ $$

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