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Question Number 86379 Answers: 1 Comments: 2

Question Number 86375 Answers: 1 Comments: 2

calculate by complex method ∫_0 ^∞ (dx/(x^2 −x+1))

$${calculate}\:{by}\:{complex}\:{method}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}} \\ $$

Question Number 86365 Answers: 0 Comments: 0

I think it will be ∫_0 ^(π/4) (dx/(√(1+tanx))) ≈∫_0 ^(π/4) (dx/(√(1+x))) =(𝛑/4)−(1/2).(1/2).((𝛑/4))^2 +((1.3)/(2.4)).(1/3).((𝛑/4))^3 −((1.3.5)/(2.4.6)).(1/4)((𝛑/4))^4 +....

$$\mathrm{I}\:\mathrm{think}\:\mathrm{it}\:\mathrm{will}\:\mathrm{be} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{dx}}{\sqrt{\mathrm{1}+\mathrm{tanx}}}\:\approx\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{dx}}{\sqrt{\mathrm{1}+\mathrm{x}}}\: \\ $$$$=\frac{\boldsymbol{\pi}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{2}}.\frac{\mathrm{1}}{\mathrm{2}}.\left(\frac{\boldsymbol{\pi}}{\mathrm{4}}\right)^{\mathrm{2}} +\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}.\mathrm{4}}.\frac{\mathrm{1}}{\mathrm{3}}.\left(\frac{\boldsymbol{\pi}}{\mathrm{4}}\right)^{\mathrm{3}} −\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}.\mathrm{4}.\mathrm{6}}.\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\boldsymbol{\pi}}{\mathrm{4}}\right)^{\mathrm{4}} +.... \\ $$

Question Number 86361 Answers: 0 Comments: 2

mr.w can you check question no.76808

$${mr}.{w}\:{can}\:{you}\:{check} \\ $$$${question}\:{no}.\mathrm{76808} \\ $$

Question Number 86358 Answers: 0 Comments: 1

Question Number 86356 Answers: 1 Comments: 1

Question Number 86349 Answers: 0 Comments: 1

mr.aliesam can you check the answer of 76808

$${mr}.{aliesam}\:{can}\:{you} \\ $$$${check}\:\:{the}\:{answer}\:{of} \\ $$$$\mathrm{76808} \\ $$

Question Number 86346 Answers: 1 Comments: 2

Question Number 86343 Answers: 0 Comments: 2

Dear mr w. i want discuss for equation find minimum and maximum value of xy +2 with constraint x^2 +y^(2 ) = 6. my way (short cut) ⇒ x^2 = y^2 = 3 { ((max = ((√3))^2 +2 = 5)),((min = −((√3))^2 +1 = −1)) :} it correct?

$$\mathrm{Dear}\:\mathrm{mr}\:\mathrm{w}.\:\mathrm{i}\:\mathrm{want}\: \\ $$$$\mathrm{discuss}\:\mathrm{for}\:\mathrm{equation} \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{xy}\:+\mathrm{2}\:\mathrm{with}\:\mathrm{constraint} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}\:} =\:\mathrm{6}. \\ $$$$\mathrm{my}\:\mathrm{way}\:\left(\mathrm{short}\:\mathrm{cut}\right) \\ $$$$\Rightarrow\:\mathrm{x}^{\mathrm{2}} \:=\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{3} \\ $$$$\begin{cases}{\mathrm{max}\:=\:\left(\sqrt{\mathrm{3}}\right)^{\mathrm{2}} +\mathrm{2}\:=\:\mathrm{5}}\\{\mathrm{min}\:=\:−\left(\sqrt{\mathrm{3}}\right)^{\mathrm{2}} \:+\mathrm{1}\:=\:−\mathrm{1}}\end{cases} \\ $$$$\mathrm{it}\:\mathrm{correct}? \\ $$

Question Number 86341 Answers: 0 Comments: 0

Can anyone pls check question no. 76808

$${Can}\:{anyone}\:{pls}\:{check}\: \\ $$$${question}\:{no}.\:\mathrm{76808} \\ $$

Question Number 86339 Answers: 1 Comments: 0

4^x +6^x =9^x

$$\mathrm{4}^{{x}} +\mathrm{6}^{{x}} =\mathrm{9}^{{x}} \\ $$$$ \\ $$$$ \\ $$

Question Number 86337 Answers: 0 Comments: 1

$$\left[\mathrm{4}\right. \\ $$

Question Number 86328 Answers: 1 Comments: 0

∫((x^2 −1)/((x^2 +1)(√(1+x^4 )))) dx

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

Question Number 86326 Answers: 0 Comments: 0

Let f a continue function acknowleding α as a fix point on [0,1].F a function such as (dF/dx)=f(x) ∀ n , u_(n+1) =((F(u_n )−F(α))/(u_n −α)) Prove that lim_(n→∞) u_n =α

$${Let}\:{f}\:{a}\:{continue}\:{function}\:{acknowleding} \\ $$$$\alpha\:{as}\:{a}\:{fix}\:{point}\:{on}\:\left[\mathrm{0},\mathrm{1}\right].{F}\:\:{a}\:{function}\:{such}\:{as}\:\frac{{dF}}{{dx}}={f}\left({x}\right) \\ $$$$\forall\:{n}\:,\:\:{u}_{{n}+\mathrm{1}} =\frac{{F}\left({u}_{{n}} \right)−{F}\left(\alpha\right)}{{u}_{{n}} −\alpha}\: \\ $$$${Prove}\:{that}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{u}_{{n}} \:=\alpha \\ $$

Question Number 86324 Answers: 0 Comments: 2

∫_( 0) ^( (π/4)) ((1 )/((√(sin x)) + (√(cos x)))) dx

$$\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \:\frac{\mathrm{1}\:}{\sqrt{\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}}\:\:\:+\:\:\sqrt{\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}}}\:\boldsymbol{\mathrm{dx}} \\ $$

Question Number 86313 Answers: 2 Comments: 2

∫_0 ^(π/2) (dx/(√(1+tan x)))

$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{{dx}}{\sqrt{\mathrm{1}+\mathrm{tan}\:{x}}} \\ $$

Question Number 86307 Answers: 1 Comments: 0

Solve the following equation: (d^2 y/dx^2 ) −2 (dy/dx) +y = x e^x sin x.

$$\:\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:−\mathrm{2}\:\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:+\boldsymbol{\mathrm{y}}\:=\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} \:\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}. \\ $$

Question Number 86302 Answers: 1 Comments: 1

∫ (dx/((x^2 +1)(√(x^2 +4)))) =?