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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

Question Number 53522 Answers: 1 Comments: 0

Cost of 2 pencils and 3 erasers is Rs.18, while the cost of 1 pencil and 2 erasers is Rs. 11. Find the cost of each pencil.

$$\mathrm{Cost}\:\mathrm{of}\:\:\mathrm{2}\:\mathrm{pencils}\:\mathrm{and}\:\:\mathrm{3}\:\mathrm{erasers}\:\mathrm{is}\:\mathrm{Rs}.\mathrm{18}, \\ $$$$\mathrm{while}\:\mathrm{the}\:\mathrm{cost}\:\mathrm{of}\:\:\mathrm{1}\:\:\mathrm{pencil}\:\mathrm{and}\:\:\mathrm{2}\:\mathrm{erasers} \\ $$$$\mathrm{is}\:\mathrm{Rs}.\:\mathrm{11}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{cost}\:\mathrm{of}\:\mathrm{each}\:\mathrm{pencil}. \\ $$

Question Number 53518 Answers: 2 Comments: 0

Find the sum of 3.2^− and 5.4^− .

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\:\mathrm{3}.\overset{−} {\mathrm{2}}\:\:\mathrm{and}\:\:\mathrm{5}.\overset{−} {\mathrm{4}}\:\:. \\ $$

Question Number 53515 Answers: 1 Comments: 0

What is the sum of ten odd numbers and eleven even numbers?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{ten}\:\mathrm{odd}\:\mathrm{numbers} \\ $$$$\mathrm{and}\:\mathrm{eleven}\:\mathrm{even}\:\mathrm{numbers}? \\ $$

Question Number 53514 Answers: 0 Comments: 0

What is the sum of ten odd numbers and eleven even numbers?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{ten}\:\mathrm{odd}\:\mathrm{numbers} \\ $$$$\mathrm{and}\:\mathrm{eleven}\:\mathrm{even}\:\mathrm{numbers}? \\ $$

Question Number 53513 Answers: 0 Comments: 0

What is the sum of ten odd numbers and eleven even numbers?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{ten}\:\mathrm{odd}\:\mathrm{numbers} \\ $$$$\mathrm{and}\:\mathrm{eleven}\:\mathrm{even}\:\mathrm{numbers}? \\ $$

Question Number 53502 Answers: 2 Comments: 0

If (x−5) is a factor of 2x^2 +2px−2p=0, the value of p is

$$\mathrm{If}\:\left({x}−\mathrm{5}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{factor}\:\mathrm{of}\:\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{px}−\mathrm{2}{p}=\mathrm{0}, \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:{p}\:\:\mathrm{is} \\ $$

Question Number 53501 Answers: 0 Comments: 0

If (x−5) is a factor of 2x^2 +2px−2p=0, the value of p is

$$\mathrm{If}\:\left({x}−\mathrm{5}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{factor}\:\mathrm{of}\:\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{px}−\mathrm{2}{p}=\mathrm{0}, \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:{p}\:\:\mathrm{is} \\ $$

Question Number 53500 Answers: 2 Comments: 0

1. If (√((x+2)^(2 ) +y^2 ))+(√((x−2)^2 +y^2 ))=6 show that when the equation is simplified, it can be express as (x^2 /9)+(y^2 /5)=1 2. find the value of n such that the linear factors of the form x+ay+b and x+cy+d with integer coefficients have the product x^2 +5xy+x+ny−n sir please help

$$\mathrm{1}.\:{If}\:\:\sqrt{\left({x}+\mathrm{2}\right)^{\mathrm{2}\:} +{y}^{\mathrm{2}} }+\sqrt{\left({x}−\mathrm{2}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} }=\mathrm{6} \\ $$$${show}\:{that}\:{when}\:{the}\:{equation}\:{is}\: \\ $$$${simplified},\:{it}\:{can}\:{be}\:{express}\:{as} \\ $$$$\frac{{x}^{\mathrm{2}} }{\mathrm{9}}+\frac{{y}^{\mathrm{2}} }{\mathrm{5}}=\mathrm{1} \\ $$$$\mathrm{2}.\:{find}\:{the}\:{value}\:{of}\:{n}\:{such}\:{that}\:{the} \\ $$$${linear}\:{factors}\:{of}\:{the}\:{form}\:{x}+{ay}+{b}\: \\ $$$${and}\:{x}+{cy}+{d}\:{with}\:{integer}\:{coefficients} \\ $$$${have}\:{the}\:{product}\:{x}^{\mathrm{2}} +\mathrm{5}{xy}+{x}+{ny}−{n} \\ $$$${sir}\:{please}\:{help} \\ $$

Question Number 53492 Answers: 1 Comments: 1

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