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Question Number 72495 Answers: 0 Comments: 3

lim_(x→∞) (((lnx)/x))^((lnx)/x) =?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{{lnx}}{{x}}\right)^{\frac{{lnx}}{{x}}} =? \\ $$

Question Number 72494 Answers: 1 Comments: 1

((∫x(√(x^2 +5)) dx−3∫(x/(√(x^2 +5)))dx)/(∫((x(x^2 +2))/(√(x^2 +5))) dx))

$$\frac{\int{x}\sqrt{{x}^{\mathrm{2}} +\mathrm{5}}\:{dx}−\mathrm{3}\int\frac{{x}}{\sqrt{{x}^{\mathrm{2}} +\mathrm{5}}}{dx}}{\int\frac{{x}\left({x}^{\mathrm{2}} +\mathrm{2}\right)}{\sqrt{{x}^{\mathrm{2}} +\mathrm{5}}}\:{dx}} \\ $$

Question Number 72492 Answers: 3 Comments: 1

(1/(cosx))+(1/(sinx))=8 find the value of x

$$\frac{\mathrm{1}}{\mathrm{cosx}}+\frac{\mathrm{1}}{\mathrm{sinx}}=\mathrm{8} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$

Question Number 72488 Answers: 2 Comments: 0

{ ((4xy=1)),((4(√(1−x^2 )) ( y−(√(1−y^2 )) )=1)) :} Resolver elsistema en R

$$\begin{cases}{\mathrm{4}{xy}=\mathrm{1}}\\{\mathrm{4}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:\left(\:{y}−\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }\:\right)=\mathrm{1}}\end{cases} \\ $$$$ \\ $$$${Resolver}\:{elsistema}\:{en}\:{R} \\ $$

Question Number 72483 Answers: 2 Comments: 0

Σ_(k = 0) ^n cos(a + kb)

$$\underset{\mathrm{k}\:=\:\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\:\mathrm{cos}\left(\mathrm{a}\:+\:\mathrm{kb}\right) \\ $$

Question Number 72479 Answers: 0 Comments: 1

Question Number 72466 Answers: 1 Comments: 2

Prove that ∫_0 ^( 2) ∫_(−(√(1−(y−1)^2 ))) ^( 0 ) xy^2 dxdy = −(4/5) after changing the integral to polar form.

$${Prove}\:{that}\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \int_{−\sqrt{\mathrm{1}−\left({y}−\mathrm{1}\right)^{\mathrm{2}} }} ^{\:\:\mathrm{0}\:} \:{xy}^{\mathrm{2}} {dxdy}\:=\:−\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\boldsymbol{{after}}\:\mathrm{changing}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{to}\:\boldsymbol{\mathrm{polar}}\:\boldsymbol{\mathrm{form}}. \\ $$

Question Number 72458 Answers: 0 Comments: 0

Question Number 72453 Answers: 0 Comments: 0

Question Number 72447 Answers: 1 Comments: 0

Find the value of: (1/(sin 2°))+(1/(sin 4°))+(1/(sin 8°))+(1/(sin 16°))+... +(1/(sin (2^(1029) )^° ))

$${Find}\:{the}\:{value}\:{of}: \\ $$$$\frac{\mathrm{1}}{{sin}\:\mathrm{2}°}+\frac{\mathrm{1}}{{sin}\:\mathrm{4}°}+\frac{\mathrm{1}}{{sin}\:\mathrm{8}°}+\frac{\mathrm{1}}{{sin}\:\mathrm{16}°}+... \\ $$$$+\frac{\mathrm{1}}{{sin}\:\left(\mathrm{2}^{\mathrm{1029}} \right)^{°} } \\ $$

Question Number 72434 Answers: 1 Comments: 0

Question Number 72435 Answers: 0 Comments: 1

Question Number 72430 Answers: 0 Comments: 0

Hello find finde ∫_0 ^(+∞) ((ln(x))/(x^2 +ax+b))dx conditions a^2 <4b in therm of x_1 ,x_2 root of X^2 +aX+b hint Residus theorem applied too ((log^2 (z))/(z^2 +az+b)) this is very usufull i find it in lecture yesterday because we can easly evaluat any kinde of ∫_0 ^(+∞) ((log^k (z))/(p(z)))dz withe p(z) eiwthout root in ]0,+∞[ deg(p(z))≥2

$$\mathrm{Hello}\:\mathrm{find} \\ $$$$\mathrm{finde}\:\:\int_{\mathrm{0}} ^{+\infty} \frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{ax}+\mathrm{b}}\mathrm{dx} \\ $$$$\mathrm{conditions}\:\mathrm{a}^{\mathrm{2}} <\mathrm{4b}\:\:\: \\ $$$$\mathrm{in}\:\mathrm{therm}\:\mathrm{of}\:\mathrm{x}_{\mathrm{1}} ,\mathrm{x}_{\mathrm{2}} \:\:\mathrm{root}\:\mathrm{of}\:\mathrm{X}^{\mathrm{2}} +\mathrm{aX}+\mathrm{b}\: \\ $$$$\:\mathrm{hint}\:\mathrm{Residus}\:\mathrm{theorem}\:\mathrm{applied}\:\mathrm{too}\:\frac{\mathrm{log}^{\mathrm{2}} \left(\mathrm{z}\right)}{\mathrm{z}^{\mathrm{2}} +\mathrm{az}+\mathrm{b}} \\ $$$$\mathrm{this}\:\mathrm{is}\:\mathrm{very}\:\mathrm{usufull}\:\mathrm{i}\:\mathrm{find}\:\mathrm{it}\:\mathrm{in}\:\mathrm{lecture}\:\mathrm{yesterday} \\ $$$$\mathrm{because}\:\mathrm{we}\:\mathrm{can}\:\mathrm{easly}\:\mathrm{evaluat}\:\mathrm{any}\:\mathrm{kinde}\:\mathrm{of}\:\int_{\mathrm{0}} ^{+\infty} \frac{\mathrm{log}^{\mathrm{k}} \left(\mathrm{z}\right)}{\mathrm{p}\left(\mathrm{z}\right)}\mathrm{dz} \\ $$$$\left.\mathrm{withe}\:\mathrm{p}\left(\mathrm{z}\right)\:\mathrm{eiwthout}\:\:\mathrm{root}\:\mathrm{in}\:\right]\mathrm{0},+\infty\left[\:\mathrm{deg}\left(\mathrm{p}\left(\mathrm{z}\right)\right)\geqslant\mathrm{2}\right. \\ $$

Question Number 72445 Answers: 0 Comments: 0

∫((x cos(ax))/(1+x^2 )) dx

$$\int\frac{{x}\:{cos}\left({ax}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$

Question Number 72443 Answers: 1 Comments: 0

2[0.5{48−31}^2 +35]=?

$$\mathrm{2}\left[\mathrm{0}.\mathrm{5}\left\{\mathrm{48}−\mathrm{31}\right\}^{\mathrm{2}} +\mathrm{35}\right]=? \\ $$

Question Number 72441 Answers: 2 Comments: 1

If^n C_(12) =^n C_8 , then n=

$$\mathrm{If}\:^{{n}} {C}_{\mathrm{12}} =\:^{{n}} {C}_{\mathrm{8}} \:,\:\mathrm{then}\:{n}= \\ $$

Question Number 72439 Answers: 0 Comments: 1