Question and Answers Forum

AllQuestion and Answers: Page 1461

Question Number 64640 Answers: 1 Comments: 3

I = Σ_(n = 0) ^∞ (((− 1)^n )/(6n + 1))

$$\mathrm{I}\:\:=\:\:\underset{\mathrm{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\left(−\:\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{6n}\:+\:\mathrm{1}} \\ $$

Question Number 64635 Answers: 0 Comments: 1

1)calculate f(a) =∫_0 ^∞ ((arctan(αx))/(1+x^2 ))dx with α real 2) find the value of ∫_0 ^∞ ((arctan(2x))/(1+x^2 ))dx

$$\left.\mathrm{1}\right){calculate}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:\:{with}\:\alpha\:{real} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 64631 Answers: 1 Comments: 3

(√((1+2x(√(1−x^2 )))/2))+2x^2 =1 To solve in R

$$\sqrt{\frac{\mathrm{1}+\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{\mathrm{2}}}+\mathrm{2}{x}^{\mathrm{2}} =\mathrm{1} \\ $$$$\mathrm{To}\:\mathrm{solve}\:\mathrm{in}\:\mathbb{R} \\ $$

Question Number 64625 Answers: 2 Comments: 3

Question Number 64619 Answers: 0 Comments: 2

show that ∫_(−α) ^α sinc(x)dx=∫_(−α) ^α sinc^2 (x)dx=Π

$${show}\:{that}\:\int_{−\alpha} ^{\alpha} {sinc}\left({x}\right){dx}=\int_{−\alpha} ^{\alpha} {sinc}^{\mathrm{2}} \left({x}\right){dx}=\Pi \\ $$

Question Number 64612 Answers: 0 Comments: 3

Question Number 64610 Answers: 0 Comments: 2

Question Number 64591 Answers: 0 Comments: 0

Question Number 64604 Answers: 0 Comments: 0

find all integr naturals n and k wich verify k!=(2^n −1)(2^n −2)(2^n −4)...(2^n −2^(n−1) )

$${find}\:\:{all}\:{integr}\:{naturals}\:{n}\:{and}\:{k}\:{wich}\:{verify} \\ $$$${k}!=\left(\mathrm{2}^{{n}} −\mathrm{1}\right)\left(\mathrm{2}^{{n}} −\mathrm{2}\right)\left(\mathrm{2}^{{n}} −\mathrm{4}\right)...\left(\mathrm{2}^{{n}} −\mathrm{2}^{{n}−\mathrm{1}} \right) \\ $$

Question Number 64601 Answers: 1 Comments: 0

10^x =x^(1000) ⇒ x =?

$$\:\:\:\:\:\mathrm{10}^{{x}} ={x}^{\mathrm{1000}} \:\Rightarrow\:{x}\:=? \\ $$

Question Number 64671 Answers: 0 Comments: 1

Question Number 64580 Answers: 3 Comments: 0

a^2 +b^2 =a+b ,a^2 −b^2 =ab a=? b=? and what if a^2 +b^2 =a−b?

$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={a}+{b}\:,{a}^{\mathrm{2}} −{b}^{\mathrm{2}} ={ab} \\ $$$${a}=?\:{b}=? \\ $$$${and}\:{what}\:{if}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={a}−{b}? \\ $$

Question Number 64579 Answers: 0 Comments: 1

∫ e^x^2 dx can we get a close form of this integral or analytic solution

$$\int\:\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \:\mathrm{dx} \\ $$$$ \\ $$$$\mathrm{can}\:\mathrm{we}\:\mathrm{get}\:\mathrm{a}\:\mathrm{close}\:\mathrm{form}\:\mathrm{of}\:\mathrm{this}\:\mathrm{integral}\:\mathrm{or}\:\mathrm{analytic}\:\mathrm{solution} \\ $$

Question Number 64574 Answers: 0 Comments: 7

Question Number 64564 Answers: 0 Comments: 2

Question Number 64561 Answers: 1 Comments: 1

Question Number 64559 Answers: 0 Comments: 1

Question Number 64557 Answers: 1 Comments: 3

Question Number 64544 Answers: 1 Comments: 1

Question Number 64545 Answers: 2 Comments: 2

Question Number 64542 Answers: 2 Comments: 0

Question Number 64541 Answers: 1 Comments: 0

lol....QUESTION OF THE DAY SHOW FULL WORKINGS ∫x((((1−x^2 )Ln(1+x^2 )+(1+x^2 )−(1−x^2 )Ln(1−x^2 ))/((1−x^4 )(1+x^2 ))))e^((x^2 −1)/(x^2 +1)) dx

$${lol}....{QUESTION}\:{OF}\:\:{THE}\:{DAY} \\ $$$$ \\ $$$${SHOW}\:{FULL}\:{WORKINGS} \\ $$$$ \\ $$$$\int{x}\left(\frac{\left(\mathrm{1}−{x}^{\mathrm{2}} \right){Ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)+\left(\mathrm{1}+{x}^{\mathrm{2}} \right)−\left(\mathrm{1}−{x}^{\mathrm{2}} \right){Ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)}{\left(\mathrm{1}−{x}^{\mathrm{4}} \right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}\right){e}^{\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}} {dx} \\ $$

Question Number 64539 Answers: 1 Comments: 9

lim_(xat 0) [cos^2 (4x)]/x^2 −lim_(x at 0) [cos^3 (6x)]/x^2

$${lim}_{{xat}\:\mathrm{0}} \left[{cos}^{\mathrm{2}} \left(\mathrm{4}{x}\right)\right]/{x}^{\mathrm{2}} \:\:−{lim}_{{x}\:{at}\:\mathrm{0}} \left[{cos}^{\mathrm{3}} \left(\mathrm{6}{x}\right)\right]/{x}^{\mathrm{2}} \\ $$

Question Number 64534 Answers: 0 Comments: 1

evalate y= 3e^(4x) − (5/(3e^(3x ) )) + 4lin2x at points (a) (0 4) and (1 8).

$${evalate}\:{y}=\:\mathrm{3}{e}^{\mathrm{4}{x}} \:−\:\frac{\mathrm{5}}{\mathrm{3}{e}^{\mathrm{3}{x}\:} }\:+\:\mathrm{4}{lin}\mathrm{2}{x}\:{at}\:\: \\ $$$${points}\:\left({a}\right)\:\left(\mathrm{0}\:\mathrm{4}\right)\:{and}\:\left(\mathrm{1}\:\mathrm{8}\right). \\ $$

Question Number 64533 Answers: 1 Comments: 0

Find all solutions of x real numbers such that 2x^2 − 7x + 6 = 15 ⌊(1/x)⌋⌊x⌋

$${Find}\:\:{all}\:\:{solutions}\:\:{of}\:\:{x}\:\:{real}\:\:{numbers}\:\:{such}\:\:{that} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} \:−\:\mathrm{7}{x}\:+\:\mathrm{6}\:\:=\:\:\mathrm{15}\:\lfloor\frac{\mathrm{1}}{{x}}\rfloor\lfloor{x}\rfloor \\ $$

Question Number 64529 Answers: 0 Comments: 0

calculate ∫_1 ^2 (dx/(√x)) by Rieman sum.

$${calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\frac{{dx}}{\sqrt{{x}}}\:\:\:{by}\:{Rieman}\:{sum}. \\ $$

Pg 1456 Pg 1457 Pg 1458 Pg 1459 Pg 1460 Pg 1461 Pg 1462 Pg 1463 Pg 1464 Pg 1465

Contact: info@tinkutara.com