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Question Number 81482 Answers: 1 Comments: 1

Evaluate ∫_(−∞) ^∞ (dx/(x^2 +4x+13)).

$${Evaluate}\:\:\int_{−\infty} ^{\infty} \frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{13}}. \\ $$

Question Number 81471 Answers: 0 Comments: 1

prove that tan (x) = sinh (y) if sin (x)= tanh (y).

$$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\mathrm{tan}\:\left(\mathrm{x}\right)\:=\:\mathrm{sinh}\:\left(\mathrm{y}\right)\:\mathrm{if}\:\mathrm{sin}\:\left(\mathrm{x}\right)= \\ $$$$\mathrm{tanh}\:\left(\mathrm{y}\right). \\ $$

Question Number 81470 Answers: 1 Comments: 0

Prove that the locus of the point of intersection of perpendicular tangents to an ellipse is another ellipse.

$${Prove}\:{that}\:{the}\:{locus}\:{of}\:{the}\:{point} \\ $$$${of}\:{intersection}\:{of}\:{perpendicular} \\ $$$${tangents}\:{to}\:{an}\:{ellipse}\:{is}\:{another} \\ $$$${ellipse}. \\ $$

Question Number 81467 Answers: 1 Comments: 1

Question Number 81458 Answers: 0 Comments: 2

if a_1 = 3 ,a_2 =2 a_(n+2) = a_(n+1) +(a_1 /2) find a_6 =? mister W method a_n =A(((1+(√3))/2))^n +B(((1−(√3))/2))^n a_1 = A(((1+(√3))/2))+B(((1−(√3))/2))=3 a_2 = A(((1+(√3))/2))^2 +B(((1−(√3))/2))^2 =2 ⇒A+B+(A−B)(√3) =6 ⇒2(A+B)+(A−B)(√3) =4 A= ((4−(√3))/(√3)) , B = ((−4−(√3))/3) a_n = (((4−(√3))/(√3)))(((1+(√3))/2))^n −(((4+(√3))/(√3)))(((1−(√3))/2))^n

Question Number 81446 Answers: 0 Comments: 5

given a_1 = 2 , a_2 = 3 and a_(n+2) = a_(n+1) + (a_n /2) find a_n =?

$$\mathrm{given}\:\mathrm{a}_{\mathrm{1}} \:=\:\mathrm{2}\:,\:\mathrm{a}_{\mathrm{2}} \:=\:\mathrm{3}\:\mathrm{and} \\ $$$$\mathrm{a}_{\mathrm{n}+\mathrm{2}} \:=\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:+\:\frac{\mathrm{a}_{\mathrm{n}} }{\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{a}_{\mathrm{n}} \:=? \\ $$

Question Number 81445 Answers: 0 Comments: 0

Question Number 81439 Answers: 0 Comments: 2

f(x) = x^2 e^x f^((100)) (0) = ?

$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{2}} \:\mathrm{e}^{\mathrm{x}} \\ $$$$\mathrm{f}^{\left(\mathrm{100}\right)} \left(\mathrm{0}\right)\:=\:? \\ $$

Question Number 81437 Answers: 0 Comments: 1

5^(lnx) = 50 −x^(ln 5)

$$\mathrm{5}\:^{\mathrm{lnx}} \:=\:\mathrm{50}\:−\mathrm{x}^{\mathrm{ln}\:\mathrm{5}} \\ $$$$ \\ $$

Question Number 81435 Answers: 2 Comments: 6

Question Number 81434 Answers: 1 Comments: 2

find U_n =∫_1 ^n arctan(x+(1/x))dx and determine nature of Σ U_n

$${find}\:{U}_{{n}} \:=\int_{\mathrm{1}} ^{{n}} \:{arctan}\left({x}+\frac{\mathrm{1}}{{x}}\right){dx} \\ $$$${and}\:{determine}\:{nature}\:{of}\:\Sigma\:{U}_{{n}} \\ $$

Question Number 81433 Answers: 1 Comments: 0

calculate ∫_2 ^(+∞) ((2x+3)/((x−1)^3 (x^2 +x+1)^2 ))dx

$${calculate}\:\int_{\mathrm{2}} ^{+\infty} \:\:\:\:\:\frac{\mathrm{2}{x}+\mathrm{3}}{\left({x}−\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 81432 Answers: 1 Comments: 1

find ∫ (dx/((x+1)^3 (x^2 +3)^2 ))

$${find}\:\:\int\:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} } \\ $$

Question Number 81431 Answers: 0 Comments: 2

let f(x)=((arctan(2x))/(1+x)) 1) calculate f^((n)) (x) and f^((n)) (0) 2) developp f at integr serie

$${let}\:{f}\left({x}\right)=\frac{{arctan}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{x}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$

Question Number 81430 Answers: 0 Comments: 1

let the matrix A= (((1 2)),((−1 3)) ) 1) calculste A^n 2) find e^A and e^(−A) 3)find cosA and sinA

$${let}\:{the}\:{matrix}\:{A}=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\mathrm{2}}\\{−\mathrm{1}\:\:\:\mathrm{3}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculste}\:{A}^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{e}^{{A}} \:{and}\:{e}^{−{A}} \\ $$$$\left.\mathrm{3}\right){find}\:{cosA}\:{and}\:{sinA} \\ $$

Question Number 81429 Answers: 0 Comments: 0

calculate lim_(x→0) ((sin(shx)−sh(sinx))/x^2 )

$${calculate}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{sin}\left({shx}\right)−{sh}\left({sinx}\right)}{{x}^{\mathrm{2}} } \\ $$

Question Number 81428 Answers: 1 Comments: 0

calculate lim_(x→+∞) x^3 ln(1+e^(−x^2 ) )

$${calculate}\:{lim}_{{x}\rightarrow+\infty} \:{x}^{\mathrm{3}} {ln}\left(\mathrm{1}+{e}^{−{x}^{\mathrm{2}} } \right) \\ $$

Question Number 81427 Answers: 1 Comments: 4

1) calculate ∫_0 ^∞ cos(x^3 )dx 2)find the value of ∫_0 ^∞ cos(x^n )dx with n≥2

$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{\mathrm{3}} \right){dx} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{{n}} \right){dx}\:{with}\:{n}\geqslant\mathrm{2} \\ $$

Question Number 81421 Answers: 1 Comments: 1

Question Number 81400 Answers: 1 Comments: 3

Hello Nice day im thinking of this one a close forme? ∫(√(1+x^p ))dx p∈R_+ , x∈[0,1[

$${Hello}\:\:{Nice}\:{day}\:{im}\:{thinking}\:{of}\:{this}\:{one}\:\:{a}\:{close}\:{forme}? \\ $$$$\int\sqrt{\mathrm{1}+{x}^{{p}} }{dx} \\ $$$${p}\in\mathbb{R}_{+} , \\ $$$${x}\in\left[\mathrm{0},\mathrm{1}\left[\right.\right. \\ $$

Question Number 81393 Answers: 2 Comments: 1

Question Number 81404 Answers: 0 Comments: 0

Question Number 81403 Answers: 1 Comments: 1

Solve x ∈ R such that (((x+1)^5 )/((x^5 + 1))) = ((81)/(11))

$${Solve}\:\:{x}\:\in\:\mathbb{R}\:\:\:{such}\:\:{that} \\ $$$$\frac{\left({x}+\mathrm{1}\right)^{\mathrm{5}} }{\left({x}^{\mathrm{5}} \:+\:\mathrm{1}\right)}\:\:=\:\:\frac{\mathrm{81}}{\mathrm{11}} \\ $$

Question Number 81369 Answers: 2 Comments: 7

Question Number 81364 Answers: 0 Comments: 2

log_2 (log_3 (log_2 (2/x))−1) < 1 has solution (1/a^(26) )<x<b. find a ?

$$\mathrm{log}_{\mathrm{2}} \:\left(\mathrm{log}_{\mathrm{3}} \:\left(\mathrm{log}_{\mathrm{2}} \:\frac{\mathrm{2}}{\mathrm{x}}\right)−\mathrm{1}\right)\:<\:\mathrm{1}\: \\ $$$$\mathrm{has}\:\mathrm{solution}\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{26}} }<\mathrm{x}<\mathrm{b}.\:\mathrm{find}\:\mathrm{a}\:? \\ $$

Question Number 81354 Answers: 0 Comments: 2

given y = sin ((π/3)−2x)+2cos ((π/(12))+x)+1 where x ∈(0,2π) has maximum and minimum value is p and q. find p^2 −q^2 ? (A) −18 (B) −16 (C) ((63)/4) (D) 16

$$\mathrm{given}\:\mathrm{y}\:=\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{3}}−\mathrm{2x}\right)+\mathrm{2cos}\:\left(\frac{\pi}{\mathrm{12}}+\mathrm{x}\right)+\mathrm{1} \\ $$$$\mathrm{where}\:\mathrm{x}\:\in\left(\mathrm{0},\mathrm{2}\pi\right)\:\mathrm{has}\:\mathrm{maximum}\:\mathrm{and} \\ $$$$\mathrm{minimum}\:\mathrm{value}\:\mathrm{is}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}. \\ $$$$\mathrm{find}\:\mathrm{p}^{\mathrm{2}} −\mathrm{q}^{\mathrm{2}} \:? \\ $$$$\left(\mathrm{A}\right)\:−\mathrm{18}\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:−\mathrm{16} \\ $$$$\left(\mathrm{C}\right)\:\frac{\mathrm{63}}{\mathrm{4}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{16} \\ $$

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