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Question Number 53688 Answers: 2 Comments: 1

i^(i ) ?? Whis is it,, plz explain it i=(√(−1))

$${i}^{{i}\:} \:?? \\ $$$${Whis}\:{is}\:{it},,\:{plz}\:{explain}\:{it} \\ $$$${i}=\sqrt{−\mathrm{1}} \\ $$

Question Number 53686 Answers: 0 Comments: 5

Question Number 53684 Answers: 1 Comments: 4

Question Number 53676 Answers: 0 Comments: 5

If (√(x^2 −1)) +(√(y^2 −1)) =(1/2)(x+y) show that (dy/dx)+(√((y^2 −1)/(x^2 −1))) =0

$${If}\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}\:+\sqrt{{y}^{\mathrm{2}} −\mathrm{1}}\:=\frac{\mathrm{1}}{\mathrm{2}}\left({x}+{y}\right) \\ $$$${show}\:{that} \\ $$$$\frac{{dy}}{{dx}}+\sqrt{\frac{{y}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}} −\mathrm{1}}}\:=\mathrm{0} \\ $$$$ \\ $$

Question Number 53675 Answers: 2 Comments: 0

Given that 1+log_3 x =log_(27) y, express y in terms of x.

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{1}+\mathrm{log}_{\mathrm{3}} \mathrm{x}\:=\mathrm{log}_{\mathrm{27}} \mathrm{y},\:\mathrm{express}\:\mathrm{y} \\ $$$$\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{x}. \\ $$

Question Number 53727 Answers: 2 Comments: 0

Question Number 53664 Answers: 1 Comments: 1

Question Number 53647 Answers: 1 Comments: 2

lim_(𝛗→∞) (1 + (1/φ))^φ = e

$$\underset{\boldsymbol{\phi}\rightarrow\infty} {\mathrm{lim}}\:\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\phi}\right)^{\phi} \:\:=\:\:\mathrm{e} \\ $$

Question Number 53630 Answers: 1 Comments: 0

Question Number 53624 Answers: 0 Comments: 0

find ∫_(−∞) ^(+∞) e^(−x^2 ) (√(1+2x^2 ))dx

$${find}\:\int_{−\infty} ^{+\infty} \:{e}^{−{x}^{\mathrm{2}} } \sqrt{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 53623 Answers: 1 Comments: 3

1) study the function f(x)=ln(x+1−(√x)) 2) determine f^(−1) (x) 3) cslculate ∫ f(x)dx snd ∫ f^(−1) (x)dx 4) dtermine ∫ f^(−1) (x^2 +f(x))dx

$$\left.\mathrm{1}\right)\:{study}\:{the}\:{function} \\ $$$${f}\left({x}\right)={ln}\left({x}+\mathrm{1}−\sqrt{{x}}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{f}^{−\mathrm{1}} \left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{cslculate}\:\:\int\:{f}\left({x}\right){dx}\:{snd} \\ $$$$\int\:{f}^{−\mathrm{1}} \left({x}\right){dx} \\ $$$$\left.\mathrm{4}\right)\:{dtermine}\:\int\:{f}^{−\mathrm{1}} \left({x}^{\mathrm{2}} \:+{f}\left({x}\right)\right){dx} \\ $$$$ \\ $$

Question Number 53621 Answers: 0 Comments: 0

How many group homomorphism exist from A_(4 ) to Z_2 ×Z_2 ?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{group}\:\mathrm{homomorphism}\:\mathrm{exist} \\ $$$$\mathrm{from}\:\mathrm{A}_{\mathrm{4}\:} \:\mathrm{to}\:\mathbb{Z}_{\mathrm{2}} ×\mathbb{Z}_{\mathrm{2}} \:\:? \\ $$

Question Number 53620 Answers: 1 Comments: 4

Σ_(n=0) ^∞ (((−1)^n )/(2n+1)) =? 1. (π/4) 2. (π^2 /(12)) 3. (π/8) 4. (π^2 /6)

$$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\:\:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{2n}+\mathrm{1}}\:=? \\ $$$$ \\ $$$$\mathrm{1}.\:\frac{\pi}{\mathrm{4}}\:\:\:\:\:\:\:\:\mathrm{2}.\:\frac{\pi^{\mathrm{2}} }{\mathrm{12}}\:\:\:\:\:\mathrm{3}.\:\frac{\pi}{\mathrm{8}}\:\:\:\:\:\mathrm{4}.\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$

Question Number 53619 Answers: 0 Comments: 0

If Σ_(n=0) ^∞ ((cosnsin(na))/n) is converge then a is? 1. a∈Z 2. a∈{kπ:k∈Z} 3. a∈R−{((2k+1)/2)π:k∈Z} 4. a∈R

$$\mathrm{If}\:\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{cosnsin}\left(\mathrm{na}\right)}{\mathrm{n}}\:\mathrm{is}\:\mathrm{converge}\:\mathrm{then}\:\mathrm{a}\:\mathrm{is}? \\ $$$$\mathrm{1}.\:\mathrm{a}\in\mathbb{Z} \\ $$$$\mathrm{2}.\:\mathrm{a}\in\left\{\mathrm{k}\pi:\mathrm{k}\in\mathbb{Z}\right\} \\ $$$$\mathrm{3}.\:\mathrm{a}\in\mathbb{R}−\left\{\frac{\mathrm{2k}+\mathrm{1}}{\mathrm{2}}\pi:\mathrm{k}\in\mathbb{Z}\right\} \\ $$$$\mathrm{4}.\:\mathrm{a}\in\mathbb{R} \\ $$$$ \\ $$

Question Number 53601 Answers: 1 Comments: 0

calculate ∫_0 ^∞ ((e^(−x^2 ) −e^(−x) )/x) dx .

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−{x}^{\mathrm{2}} } −{e}^{−{x}} }{{x}}\:{dx}\:. \\ $$

Question Number 53600 Answers: 0 Comments: 1

calculate A_m =∫_0 ^∞ ((sin(mx))/(e^(2πx) −1)) dx with m>0

$${calculate}\:{A}_{{m}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{sin}\left({mx}\right)}{{e}^{\mathrm{2}\pi{x}} −\mathrm{1}}\:{dx}\:\:{with}\:{m}>\mathrm{0} \\ $$

Question Number 53599 Answers: 0 Comments: 1

1) calculate A_n =∫_0 ^∞ (x^(n−1) /(e^x +1)) dx with n integr natural (n≥2) 2) find the value of ∫_0 ^∞ (x/(e^x +1))dx

$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{{n}−\mathrm{1}} }{{e}^{{x}} \:+\mathrm{1}}\:{dx}\:\:\:{with}\:{n}\:{integr}\:{natural}\:\:\left({n}\geqslant\mathrm{2}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{x}}{{e}^{{x}} \:+\mathrm{1}}{dx} \\ $$

Question Number 53618 Answers: 1 Comments: 3

Let x,y∈Z if x^2 +y^2 divide xy+1 then prove ((x^2 +y^2 )/(xy+1)) is square of integer number

$$\mathrm{Let}\:\mathrm{x},\mathrm{y}\in\mathbb{Z} \\ $$$$\mathrm{if}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:\mathrm{divide}\:\mathrm{xy}+\mathrm{1}\:\mathrm{then}\:\mathrm{prove} \\ $$$$\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }{\mathrm{xy}+\mathrm{1}}\:\mathrm{is}\:\mathrm{square}\:\mathrm{of}\:\mathrm{integer}\:\mathrm{number} \\ $$

Question Number 53595 Answers: 1 Comments: 5

Question Number 53593 Answers: 2 Comments: 1

Question Number 53570 Answers: 1 Comments: 7

Question Number 53556 Answers: 2 Comments: 1

Find the value of k for which the system of linear equations kx+2y=5 and 3x+y=1 has zero solutions.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:{k}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the} \\ $$$$\mathrm{system}\:\mathrm{of}\:\mathrm{linear}\:\mathrm{equations}\:\:{kx}+\mathrm{2}{y}=\mathrm{5}\: \\ $$$$\mathrm{and}\:\:\:\mathrm{3}{x}+{y}=\mathrm{1}\:\mathrm{has}\:\mathrm{zero}\:\mathrm{solutions}. \\ $$

Question Number 53550 Answers: 1 Comments: 2

Question Number 53532 Answers: 1 Comments: 1

The derivative of F (x)=∫_x^2 ^x^3 (1/(log t)) dt (x >0) is

$$\mathrm{The}\:\mathrm{derivative}\:\mathrm{of}\:{F}\:\left({x}\right)=\underset{{x}^{\mathrm{2}} } {\overset{{x}^{\mathrm{3}} } {\int}}\:\frac{\mathrm{1}}{\mathrm{log}\:{t}}\:{dt} \\ $$$$\left({x}\:>\mathrm{0}\right)\:\mathrm{is} \\ $$

Question Number 53528 Answers: 0 Comments: 0

x^3 + y^3 + z^3 = x + y + z x^2 + y^2 + z^2 = xyz x, y, z ∈ R^+ How many triple of (x, y, z) ?

$${x}^{\mathrm{3}} \:+\:{y}^{\mathrm{3}} \:+\:{z}^{\mathrm{3}} \:\:=\:\:{x}\:+\:{y}\:+\:{z} \\ $$$${x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{z}^{\mathrm{2}} \:\:=\:\:{xyz} \\ $$$${x},\:{y},\:{z}\:\:\in\:\mathbb{R}^{+} \\ $$$${How}\:\:{many}\:\:{triple}\:\:{of}\:\:\left({x},\:{y},\:{z}\right)\:\:? \\ $$

Question Number 53530 Answers: 2 Comments: 1

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