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Question Number 32722 Answers: 0 Comments: 0

find ∫_0 ^∞ (dx/(1+x^3 )) .

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{3}} }\:. \\ $$

Question Number 32702 Answers: 0 Comments: 0

Question Number 32710 Answers: 1 Comments: 0

Question Number 32709 Answers: 1 Comments: 0

Question Number 32688 Answers: 1 Comments: 0

Evaluate 1) ∫_(−1) ^0 (x^2 + x 1) dx 2) ∫_1 ^5 (x −1+ (1/x^2 ))dx

$$\mathrm{Evaluate} \\ $$$$\left.\:\mathrm{1}\right)\:\int_{−\mathrm{1}} ^{\mathrm{0}} \left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}\:\mathrm{1}\right)\:\mathrm{dx} \\ $$$$\left.\mathrm{2}\right)\:\int_{\mathrm{1}} ^{\mathrm{5}} \left(\mathrm{x}\:−\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\right)\mathrm{dx} \\ $$$$ \\ $$

Question Number 32792 Answers: 1 Comments: 2

the equation 3x− 5=15 represents a straight line. a) find one point on this line. b)find the coordinates of the points when the line cuts the x−axis and the y−axis c)find the gradient of this line.

$${the}\:{equation}\: \\ $$$$\mathrm{3}{x}−\:\mathrm{5}=\mathrm{15}\:{represents}\:{a}\:{straight}\:{line}. \\ $$$$\left.{a}\right)\:{find}\:{one}\:{point}\:{on}\:{this}\:{line}. \\ $$$$\left.{b}\right){find}\:{the}\:{coordinates}\:{of}\:{the}\:{points}\:{when} \\ $$$${the}\:{line}\:{cuts}\:{the}\:{x}−{axis}\:{and}\:{the}\:{y}−{axis} \\ $$$$\left.{c}\right){find}\:{the}\:{gradient}\:{of}\:{this}\:{line}. \\ $$$$ \\ $$

Question Number 32682 Answers: 1 Comments: 0

If x_1 and x_(2 ) are roots of the equation acos 2x+bsin x = c and 2sin x_1 sinx_2 = sin x_1 +sinx_2 . Then the value of (b/(c−a)) is ?

$$\boldsymbol{{I}}{f}\:{x}_{\mathrm{1}} \:{and}\:{x}_{\mathrm{2}\:} \:{are}\:{roots}\:{of}\:{the}\:{equation} \\ $$$${acos}\:\mathrm{2}{x}+{bsin}\:{x}\:=\:{c}\:{and}\: \\ $$$$\mathrm{2}{sin}\:{x}_{\mathrm{1}} {sinx}_{\mathrm{2}} =\:{sin}\:{x}_{\mathrm{1}} +{sinx}_{\mathrm{2}} .\:\boldsymbol{{T}}{hen}\: \\ $$$${the}\:{value}\:{of}\:\:\frac{{b}}{{c}−{a}}\:{is}\:? \\ $$

Question Number 32681 Answers: 0 Comments: 2

Total no. of polynomials of the form x^3 +ax^2 +bx+c that are divisible by x^2 +1, where a,b,c∈1,2,3,....,10 is 1) 10 2) 15 3) 5 4) 8

$$\boldsymbol{{T}}{otal}\:{no}.\:{of}\:{polynomials}\:{of}\:{the}\:{form} \\ $$$${x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c}\:\:{that}\:{are}\:{divisible}\:{by}\: \\ $$$${x}^{\mathrm{2}} +\mathrm{1},\:{where}\:{a},{b},{c}\in\mathrm{1},\mathrm{2},\mathrm{3},....,\mathrm{10}\:{is}\: \\ $$$$\left.\mathrm{1}\right)\:\mathrm{10} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{15} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{5} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{8} \\ $$

Question Number 32793 Answers: 1 Comments: 0

Given that the point (−3^ ,2) lies on the line y=2x + c.find the coordinates of the point of intersection of this line and the y−axis

$${Given}\:{that}\:{the}\:{point}\:\left(−\bar {\mathrm{3}},\mathrm{2}\right)\:{lies}\:{on}\:{the} \\ $$$${line}\:\:\:\:{y}=\mathrm{2}{x}\:+\:\mathrm{c}.{find}\:{the}\:{coordinates}\: \\ $$$${of}\:{the}\:{point}\:{of}\:{intersection}\:{of}\:{this}\:{line}\:{and}\:{the}\:{y}−{axis} \\ $$

Question Number 32679 Answers: 0 Comments: 0

If 4a^2 −5b^2 +6a+1=0 and the line ax+by+1=0 touches a fixed circle then the correct statement is : 1) centre of circle is at (3,0) 2) radius of circle is (√3). 3) circle passes through (1,0). 4) none of these.

$${If}\:\mathrm{4}{a}^{\mathrm{2}} −\mathrm{5}{b}^{\mathrm{2}} +\mathrm{6}{a}+\mathrm{1}=\mathrm{0}\:{and}\:{the}\:{line} \\ $$$${ax}+{by}+\mathrm{1}=\mathrm{0}\:{touches}\:{a}\:{fixed}\:{circle} \\ $$$${then}\:{the}\:{correct}\:{statement}\:{is}\:: \\ $$$$\left.\mathrm{1}\right)\:{centre}\:{of}\:{circle}\:{is}\:{at}\:\left(\mathrm{3},\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{radius}\:{of}\:{circle}\:{is}\:\sqrt{\mathrm{3}}. \\ $$$$\left.\mathrm{3}\right)\:{circle}\:{passes}\:{through}\:\left(\mathrm{1},\mathrm{0}\right). \\ $$$$\left.\mathrm{4}\right)\:{none}\:{of}\:{these}. \\ $$

Question Number 32794 Answers: 1 Comments: 0

given that the point (t^ ,0) lies on the curve y=2x^2 −x. find the value of t.

$${given}\:{that}\:{the}\:{point}\:\left(\bar {{t}},\mathrm{0}\right)\:{lies}\:{on}\:{the} \\ $$$${curve}\:{y}=\mathrm{2}{x}^{\mathrm{2}} −{x}.\:{find}\:{the}\:{value}\:{of}\:{t}. \\ $$

Question Number 32707 Answers: 1 Comments: 0

1)find u the value of u if Σ_(n=1) ^4 2u.2^(n−1) =64 2) find k if Σ_(n=1) ^∞ k.((1/3))^(n−1) =(2/3)

$$\left.\mathrm{1}\right)\mathrm{find}\:\mathrm{u}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{u}\:\mathrm{if} \\ $$$$\sum_{\mathrm{n}=\mathrm{1}} ^{\mathrm{4}} \mathrm{2}{u}.\mathrm{2}^{{n}−\mathrm{1}} =\mathrm{64} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{k}\:\mathrm{if}\: \\ $$$$\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \mathrm{k}.\left(\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{n}−\mathrm{1}} =\frac{\mathrm{2}}{\mathrm{3}} \\ $$

Question Number 32705 Answers: 0 Comments: 1

let give f(x)= ∫_0 ^∞ ln(1 +(x/t^2 ))dt with ∣x∣<1 find a simple form of f(x).

$${let}\:{give}\:\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:{ln}\left(\mathrm{1}\:+\frac{{x}}{{t}^{\mathrm{2}} }\right){dt}\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right). \\ $$

Question Number 32704 Answers: 0 Comments: 0

find ∫_0 ^∞ (((x+1)(√x))/(2+x^2 ))dx.