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Question Number 31414 Answers: 0 Comments: 0

find ∫_0 ^((√3) ) (dx/(x^2 +(√(x+1)))) .

$${find}\:\:\:\int_{\mathrm{0}} ^{\sqrt{\mathrm{3}}\:} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \:\:+\sqrt{{x}+\mathrm{1}}}\:. \\ $$

Question Number 31409 Answers: 1 Comments: 0

The maximum area of the triangle whose sides a,b and c satisfy 0≤a≤1 , 1≤b≤2 , 2≤c≤3 is : A) 1 B) 2 C) 1.5 D) 0.5 ?

$${The}\:{maximum}\:{area}\:{of}\:{the}\:{triangle} \\ $$$${whose}\:{sides}\:{a},{b}\:{and}\:{c}\:{satisfy}\: \\ $$$$\mathrm{0}\leqslant{a}\leqslant\mathrm{1}\:,\:\mathrm{1}\leqslant{b}\leqslant\mathrm{2}\:,\:\mathrm{2}\leqslant{c}\leqslant\mathrm{3}\:{is}\:: \\ $$$$\left.{A}\right)\:\mathrm{1} \\ $$$$\left.{B}\right)\:\mathrm{2} \\ $$$$\left.{C}\right)\:\mathrm{1}.\mathrm{5} \\ $$$$\left.{D}\right)\:\mathrm{0}.\mathrm{5}\:\:\:\:\:\:\:? \\ $$

Question Number 31406 Answers: 0 Comments: 2

Question Number 31383 Answers: 1 Comments: 6

Question Number 31382 Answers: 1 Comments: 0

Question Number 31371 Answers: 1 Comments: 0

A point moves in xy plane such that sum of its distance from two mutually perpendicular lines is always 3.The area encloded by the locus of the point is

$${A}\:{point}\:{moves}\:{in}\:{xy}\:{plane}\:{such}\: \\ $$$${that}\:{sum}\:{of}\:{its}\:{distance}\:{from}\:{two}\: \\ $$$${mutually}\:{perpendicular}\:{lines}\:{is} \\ $$$${always}\:\mathrm{3}.{The}\:{area}\:{encloded}\:{by} \\ $$$${the}\:{locus}\:{of}\:{the}\:{point}\:{is} \\ $$

Question Number 31369 Answers: 0 Comments: 0

Question Number 31350 Answers: 0 Comments: 0

Are centripetal and centrifugal forces always equal?If No,then in what conditions are they equal or not equal?

$${Are}\:{centripetal}\:{and}\:{centrifugal} \\ $$$${forces}\:{always}\:{equal}?{If}\:{No},{then} \\ $$$${in}\:{what}\:{conditions}\:{are}\:{they}\:{equal} \\ $$$${or}\:{not}\:{equal}? \\ $$

Question Number 31340 Answers: 0 Comments: 0

Deduce the power series of sin^2 x. Hence show that if x is small then (sin^2 x − x^2 cosx)/x^4 =(1/6) − (x^2 /(360))

$${Deduce}\:{the}\:{power}\:{series}\:{of}\:{sin}^{\mathrm{2}} {x}. \\ $$$${Hence}\:{show}\:{that}\:{if}\:{x}\:{is}\:{small}\:{then} \\ $$$$\left({sin}^{\mathrm{2}} {x}\:−\:{x}^{\mathrm{2}} {cosx}\right)/{x}^{\mathrm{4}} =\frac{\mathrm{1}}{\mathrm{6}}\:−\:\frac{{x}^{\mathrm{2}} }{\mathrm{360}} \\ $$

Question Number 31336 Answers: 0 Comments: 1

Find the principal value of z=(1−i)^(1+i) .Hence find the modulus of the result.

$${Find}\:{the}\:{principal}\:{value}\:{of} \\ $$$${z}=\left(\mathrm{1}−{i}\right)^{\mathrm{1}+{i}} .{Hence}\:{find}\:{the} \\ $$$${modulus}\:{of}\:{the}\:{result}. \\ $$

Question Number 31335 Answers: 0 Comments: 3

Find the pricipal value of z=(1−i)^i

$${Find}\:{the}\:{pricipal}\:{value}\:{of}\: \\ $$$${z}=\left(\mathrm{1}−{i}\right)^{{i}} \\ $$

Question Number 31329 Answers: 0 Comments: 5

Question Number 31327 Answers: 0 Comments: 1

Question Number 31326 Answers: 1 Comments: 1

Question Number 31324 Answers: 1 Comments: 0

Question Number 31323 Answers: 1 Comments: 0

Question Number 31320 Answers: 1 Comments: 0

Let p and q are the roots of x^2 − 2mx − 5n = 0 and m and n are the roots of x^2 − 2px − 5q = 0 If p ≠ q ≠ m ≠ n, then the value of p + q + m + n is ...

$$\mathrm{Let}\:{p}\:\mathrm{and}\:{q}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\: \\ $$$${x}^{\mathrm{2}} \:−\:\mathrm{2}{mx}\:−\:\mathrm{5}{n}\:=\:\mathrm{0} \\ $$$$\mathrm{and}\:{m}\:\mathrm{and}\:{n}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of} \\ $$$${x}^{\mathrm{2}} \:−\:\mathrm{2}{px}\:−\:\mathrm{5}{q}\:=\:\mathrm{0} \\ $$$$\mathrm{If}\:{p}\:\neq\:{q}\:\neq\:{m}\:\neq\:{n},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${p}\:+\:{q}\:+\:{m}\:+\:{n}\:\mathrm{is}\:... \\ $$

Question Number 31318 Answers: 1 Comments: 1

Question Number 31317 Answers: 0 Comments: 1

Question Number 31314 Answers: 0 Comments: 0

let x={(1/n)}_(n=1) ^∞ and y={(1/(n+1))}_(n=1) ^∞ be a sequence of real numbers and l_(2 ) ={x=(x_1 ,x_2 ,x_3 ,...):Σ_(n=1) ^∞ ∣xi∣^2 <∞} a linear space. (1) verify that x and y are in l_2 . (2) compute the inner product of x and y on l_2 please help me solve this question.

$${let}\:{x}=\left\{\frac{\mathrm{1}}{{n}}\right\}_{{n}=\mathrm{1}} ^{\infty} {and}\:{y}=\left\{\frac{\mathrm{1}}{{n}+\mathrm{1}}\right\}_{{n}=\mathrm{1}} ^{\infty} {be}\: \\ $$$${a}\:{sequence}\:{of}\:{real}\:{numbers}\:{and} \\ $$$${l}_{\mathrm{2}\:} =\left\{{x}=\left({x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,{x}_{\mathrm{3}} ,...\right):\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mid{xi}\mid^{\mathrm{2}} <\infty\right\} \\ $$$${a}\:{linear}\:{space}.\: \\ $$$$\left(\mathrm{1}\right)\:{verify}\:{that}\:{x}\:{and}\:{y}\:{are}\:{in}\:{l}_{\mathrm{2}} . \\ $$$$\left(\mathrm{2}\right)\:{compute}\:{the}\:{inner}\:{product}\:{of}\:{x}\: \\ $$$${and}\:{y}\:{on}\:{l}_{\mathrm{2}} \\ $$$$\boldsymbol{{please}}\:\boldsymbol{{help}}\:\boldsymbol{{me}}\:\boldsymbol{{solve}}\:\boldsymbol{{this}}\: \\ $$$$\boldsymbol{{que}}{s}\boldsymbol{{tion}}. \\ $$

Question Number 31306 Answers: 1 Comments: 0

Complete the square in y^2 +8y+9k and hence find the value of k that makes it a perfect square.

$$\mathrm{Complete}\:\mathrm{the}\:\mathrm{square}\:\mathrm{in}\:\mathrm{y}^{\mathrm{2}} \:+\mathrm{8y}+\mathrm{9k}\:\mathrm{and}\:\mathrm{hence}\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{k}\:\mathrm{that}\:\mathrm{makes}\:\mathrm{it}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}. \\ $$

Question Number 31296 Answers: 0 Comments: 11

find ∫_0 ^(+∞) (dx/((1+x^2 )^n )) with n integr and n≥1 .

$${find}\:\:\int_{\mathrm{0}} ^{+\infty} \:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }\:\:{with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{1}\:. \\ $$

Question Number 31295 Answers: 0 Comments: 0

Question Number 31289 Answers: 1 Comments: 0

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Question Number 31286 Answers: 1 Comments: 1

Find all set of ordered triple/s (x,y,z), x,y,z∈ℜ, such that x−y=1−z 3(x^2 −y^2 )=5(1−z^2 ) 7(x^3 −y^3 )=19(1−z^3 ). Please show your solution.

$${Find}\:{all}\:{set}\:{of}\:{ordered}\:{triple}/{s}\:\left({x},{y},{z}\right),\:\:{x},{y},{z}\in\Re,\:{such}\:{that} \\ $$$${x}−{y}=\mathrm{1}−{z} \\ $$$$\mathrm{3}\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)=\mathrm{5}\left(\mathrm{1}−{z}^{\mathrm{2}} \right) \\ $$$$\mathrm{7}\left({x}^{\mathrm{3}} −{y}^{\mathrm{3}} \right)=\mathrm{19}\left(\mathrm{1}−{z}^{\mathrm{3}} \right). \\ $$$${Please}\:{show}\:{your}\:{solution}. \\ $$

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