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AllQuestion and Answers: Page 1341

Question Number 76356 Answers: 0 Comments: 1

find f(x) =∫ (dt/(√(t^2 −xt +1))) with x real.

$${find}\:{f}\left({x}\right)\:=\int\:\:\frac{{dt}}{\sqrt{{t}^{\mathrm{2}} −{xt}\:+\mathrm{1}}}\:\:{with}\:{x}\:{real}. \\ $$

Question Number 76355 Answers: 2 Comments: 0

find ∫ ((arctan((√(1+x))))/(2+x))dx

$${find}\:\int\:\frac{{arctan}\left(\sqrt{\mathrm{1}+{x}}\right)}{\mathrm{2}+{x}}{dx} \\ $$

Question Number 76354 Answers: 0 Comments: 0

calculate Σ_(n=1) ^∞ (−1)^n arctan((1/(n^2 +n)))

$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \left(−\mathrm{1}\right)^{{n}} \:{arctan}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:+{n}}\right) \\ $$

Question Number 76353 Answers: 0 Comments: 1

find the value of ∫_0 ^∞ ((arctan(sin(πx^2 )))/(x^2 +π^2 ))dx

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({sin}\left(\pi{x}^{\mathrm{2}} \right)\right)}{{x}^{\mathrm{2}} \:+\pi^{\mathrm{2}} }{dx} \\ $$

Question Number 76352 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((sin(arctan(x^2 +2)))/(x^2 +1))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({arctan}\left({x}^{\mathrm{2}} +\mathrm{2}\right)\right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$

Question Number 76351 Answers: 0 Comments: 0

calculate U_n =∫_(1/n) ^1 Γ(x)dx and find lim_(n→+∞) U_n

$${calculate}\:{U}_{{n}} =\int_{\frac{\mathrm{1}}{{n}}} ^{\mathrm{1}} \:\Gamma\left({x}\right){dx}\:\:{and}\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \\ $$

Question Number 76350 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((arctan(e^x^2 ))/(x^2 +4))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({e}^{{x}^{\mathrm{2}} } \right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}{dx} \\ $$

Question Number 76346 Answers: 1 Comments: 5

Question Number 76341 Answers: 0 Comments: 1

Question Number 76340 Answers: 3 Comments: 1

Question Number 76328 Answers: 0 Comments: 2

Question Number 76326 Answers: 2 Comments: 0

Question Number 76323 Answers: 0 Comments: 2

Question Number 76317 Answers: 0 Comments: 3

Question Number 76307 Answers: 1 Comments: 0

Question Number 76306 Answers: 1 Comments: 0

z = a + bi Z = ((−7 + z)/(−3 + iz)) What is the equation of all the points M of coordonates (a,b) such as Z is real ?

$${z}\:=\:{a}\:+\:{bi} \\ $$$${Z}\:=\:\frac{−\mathrm{7}\:+\:{z}}{−\mathrm{3}\:+\:{iz}} \\ $$$$ \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{points}\:\mathrm{M} \\ $$$$\mathrm{of}\:\mathrm{coordonates}\:\left({a},{b}\right)\:\mathrm{such}\:\mathrm{as}\:{Z}\:\mathrm{is}\:\mathrm{real}\:? \\ $$

Question Number 76303 Answers: 1 Comments: 0

In the symmetric group (S_n , o), let H denotes the set of permutations leaving the integer n fixed: H = {f∈S_n ∣ f(n) = n} Show that the pair (H, o) is subgroup of (S_n ,o). ′note: the operation is composition′

$${In}\:{the}\:{symmetric}\:{group}\:\left({S}_{{n}} \:,\:{o}\right),\:{let} \\ $$$${H}\:{denotes}\:{the}\:{set}\:{of}\:{permutations}\: \\ $$$${leaving}\:{the}\:{integer}\:{n}\:{fixed}: \\ $$$$\:\:\:{H}\:=\:\left\{{f}\in{S}_{{n}} \:\mid\:{f}\left({n}\right)\:=\:{n}\right\} \\ $$$${Show}\:{that}\:{the}\:{pair}\:\left({H},\:{o}\right)\:{is}\:{subgroup} \\ $$$${of}\:\left({S}_{{n}} ,{o}\right). \\ $$$$'{note}:\:{the}\:{operation}\:{is}\:{composition}' \\ $$

Question Number 76302 Answers: 1 Comments: 0

given vektor a=(3,x,−2) b=(−6,−2,y) . what the value x and y if a and b are parallel?

$${given}\:{vektor}\:{a}=\left(\mathrm{3},{x},−\mathrm{2}\right) \\ $$$${b}=\left(−\mathrm{6},−\mathrm{2},{y}\right)\:.\:{what}\:{the}\:{value}\:{x}\: \\ $$$${and}\:{y}\:{if}\:{a}\:{and}\:{b}\:{are}\:{parallel}? \\ $$

Question Number 76298 Answers: 1 Comments: 4

∫(√( tanx+cotxdx))

$$\int\sqrt{\:\mathrm{tanx}+\mathrm{cotxdx}} \\ $$

Question Number 76290 Answers: 1 Comments: 1

how to prove x^y +y^x ≥1 , x,y ∈R x,y > 0

$$\mathrm{how}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{x}^{\mathrm{y}} \:+\mathrm{y}^{\mathrm{x}} \:\geqslant\mathrm{1}\:,\:\mathrm{x},\mathrm{y}\:\in\mathbb{R} \\ $$$$\mathrm{x},\mathrm{y}\:>\:\mathrm{0} \\ $$

Question Number 76288 Answers: 0 Comments: 2

what is f(x) if f(3)=10, f(2)=14 f(1)=20 ?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{if}\:\mathrm{f}\left(\mathrm{3}\right)=\mathrm{10},\:\mathrm{f}\left(\mathrm{2}\right)=\mathrm{14} \\ $$$$\mathrm{f}\left(\mathrm{1}\right)=\mathrm{20}\:? \\ $$

Question Number 76277 Answers: 1 Comments: 0

Question Number 76272 Answers: 1 Comments: 2

Find the area S of a triangle ABC as a function of the heights h_a , h_b and h_c .

$${Find}\:{the}\:{area}\:{S}\:{of}\:{a}\:{triangle}\:{ABC} \\ $$$${as}\:{a}\:{function}\:{of}\:{the}\:{heights} \\ $$$${h}_{{a}} ,\:{h}_{{b}} \:{and}\:{h}_{{c}} . \\ $$

Question Number 76270 Answers: 0 Comments: 5

Question Number 76265 Answers: 1 Comments: 0

Question Number 76252 Answers: 1 Comments: 1

A triangle has an area of 20 square units and two vertices are (3,4) and (2,7). What is the position of the third vertex?

$${A}\:{triangle}\:{has}\:{an}\:{area}\:{of}\:\mathrm{20}\:{square} \\ $$$${units}\:{and}\:{two}\:{vertices}\:{are}\:\left(\mathrm{3},\mathrm{4}\right)\:{and}\:\left(\mathrm{2},\mathrm{7}\right). \\ $$$${What}\:{is}\:{the}\:{position}\:{of}\:{the}\:{third}\:{vertex}? \\ $$

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