Question and Answers Forum

AllQuestion and Answers: Page 1048

Question Number 112710 Answers: 0 Comments: 0

solve ∫_0 ^1 x^2 ln(1−x)ln(1+x)dx

$${solve} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{2}} \mathrm{ln}\left(\mathrm{1}−{x}\right)\mathrm{ln}\left(\mathrm{1}+{x}\right){dx} \\ $$

Question Number 112707 Answers: 0 Comments: 0

Question Number 112697 Answers: 3 Comments: 3

....calculus... please prove : Ω=∫_0 ^( ∞) (1/((1+x^ϕ )^ϕ ))dx =1 ϕ:: golden ratio ...

$$\:\:\:\:\:....{calculus}... \\ $$$${please}\:\:{prove}\:: \\ $$$$ \\ $$$$\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{1}}{\left(\mathrm{1}+{x}^{\varphi} \right)^{\varphi} }{dx}\:=\mathrm{1} \\ $$$$\:\varphi::\:\:{golden}\:\:{ratio}\:... \\ $$

Question Number 112686 Answers: 0 Comments: 2

Question Number 112681 Answers: 1 Comments: 0

solve the equation of function (f(3x))^2 = (f(2x))^2 +(f(x))^2

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\left(\mathrm{f}\left(\mathrm{3x}\right)\right)^{\mathrm{2}} \:=\:\left(\mathrm{f}\left(\mathrm{2x}\right)\right)^{\mathrm{2}} +\left(\mathrm{f}\left(\mathrm{x}\right)\right)^{\mathrm{2}} \\ $$

Question Number 112672 Answers: 2 Comments: 2

((sin A−cos A+1)/(sin A+cos A−1)) ?

$$\:\frac{\mathrm{sin}\:\mathrm{A}−\mathrm{cos}\:\mathrm{A}+\mathrm{1}}{\mathrm{sin}\:\mathrm{A}+\mathrm{cos}\:\mathrm{A}−\mathrm{1}}\:?\: \\ $$

Question Number 112666 Answers: 2 Comments: 0

∫ tan^(−1) ((√((1−x)/(x+1)))) dx ?

$$\int\:\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{\frac{\mathrm{1}−\mathrm{x}}{\mathrm{x}+\mathrm{1}}}\right)\:\mathrm{dx}\:? \\ $$

Question Number 112664 Answers: 1 Comments: 1

what the equation of parabola whose focus F(−3,4) and directrix is 3x−4y+5=0 ?

$$\mathrm{what}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{parabola}\: \\ $$$$\mathrm{whose}\:\mathrm{focus}\:\mathrm{F}\left(−\mathrm{3},\mathrm{4}\right)\:\mathrm{and}\:\mathrm{directrix} \\ $$$$\mathrm{is}\:\mathrm{3x}−\mathrm{4y}+\mathrm{5}=\mathrm{0}\:? \\ $$

Question Number 112655 Answers: 1 Comments: 2

prove that ∞!=(√(2π))

$${prove}\:{that}\: \\ $$$$\infty!=\sqrt{\mathrm{2}\pi} \\ $$

Question Number 112651 Answers: 3 Comments: 0

(1)lim_(x→a) (x−a) cosec (((πx)/a)) ? (2) ∫ (√(x^2 +1)) dx , by using Euler′s substitution

$$\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{a}} {\mathrm{lim}}\:\left(\mathrm{x}−\mathrm{a}\right)\:\mathrm{cosec}\:\left(\frac{\pi\mathrm{x}}{\mathrm{a}}\right)\:? \\ $$$$\left(\mathrm{2}\right)\:\int\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{dx}\:,\:\mathrm{by}\:\mathrm{using}\:\mathrm{Euler}'\mathrm{s} \\ $$$$\mathrm{substitution} \\ $$

Question Number 112650 Answers: 2 Comments: 0

Determine a,b,c,d and e such that (1)lim_(x→0) ((cos ax+bx^3 +cx^2 +dx+e)/x^4 ) = (2/3) (2) find general solution : 3xy^2 y′ = 4y^3 −x^3

$$\mathrm{Determine}\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\:\mathrm{and}\:\mathrm{e}\:\mathrm{such}\:\mathrm{that} \\ $$$$\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{ax}+\mathrm{bx}^{\mathrm{3}} +\mathrm{cx}^{\mathrm{2}} +\mathrm{dx}+\mathrm{e}}{\mathrm{x}^{\mathrm{4}} }\:=\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{find}\:\mathrm{general}\:\mathrm{solution}\::\:\mathrm{3xy}^{\mathrm{2}} \:\mathrm{y}'\:=\:\mathrm{4y}^{\mathrm{3}} −\mathrm{x}^{\mathrm{3}} \: \\ $$

Question Number 112645 Answers: 2 Comments: 0

cos ((π/7))−cos (((2π)/7))+cos (((3π)/7)) =?

$$\mathrm{cos}\:\left(\frac{\pi}{\mathrm{7}}\right)−\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\:=?\: \\ $$

Question Number 112642 Answers: 1 Comments: 0

question proposed by A8;15: ∫_0 ^1 ((ln(ln(1/x)))/(1+x))dx

$${question}\:{proposed}\:{by}\:{A}\mathrm{8};\mathrm{15}: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{ln}\frac{\mathrm{1}}{{x}}\right)}{\mathrm{1}+{x}}{dx} \\ $$

Question Number 112637 Answers: 2 Comments: 0

(1)lim_(x→0) (((sinh x)/x))^(1/x^2 ) ? (2) lim_(x→0) x ln (tan x) ?

$$\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sinh}\:\mathrm{x}}{\mathrm{x}}\right)^{\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }} ? \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{x}\:\mathrm{ln}\:\left(\mathrm{tan}\:\mathrm{x}\right)\:? \\ $$

Question Number 112636 Answers: 0 Comments: 5

Question Number 112626 Answers: 1 Comments: 0

Question Number 112625 Answers: 4 Comments: 1

If a+b=5, a^2 +b^2 =13, the value of a−b (where a>b) is

$$\mathrm{If}\:\mathrm{a}+\mathrm{b}=\mathrm{5},\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} =\mathrm{13},\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{a}−\mathrm{b}\:\left(\mathrm{where}\:\mathrm{a}>\mathrm{b}\right)\:\mathrm{is} \\ $$

Question Number 112624 Answers: 3 Comments: 0

Minimum value of x^2 +(1/(x^2 +1))−3 is

$$\mathrm{Minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}−\mathrm{3}\:\mathrm{is} \\ $$

Question Number 112699 Answers: 3 Comments: 1

(1) ∫ ((sin x e^(√(cos x)) )/( (√(cos x)))) dx (2) ((1+(√(1+sin 2A)))/(1−(√(1+sin 2A))))?? (3)∫ (dx/((x+b)(x^2 +a^2 )))

$$\:\left(\mathrm{1}\right)\:\int\:\frac{\mathrm{sin}\:\mathrm{x}\:\mathrm{e}^{\sqrt{\mathrm{cos}\:\mathrm{x}}} }{\:\sqrt{\mathrm{cos}\:\mathrm{x}}}\:\mathrm{dx}\: \\ $$$$\:\left(\mathrm{2}\right)\:\frac{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{2A}}}{\mathrm{1}−\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{2A}}}??\: \\ $$$$\left(\mathrm{3}\right)\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{b}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} \right)} \\ $$

Question Number 112613 Answers: 1 Comments: 2

....number theory... Question : If a , b , c ∈ N ; then prove ::: a!∗b!∗c!∣(a+b+c)! m.n . july 970#

$$\:\:\:\:\:....{number}\:{theory}... \\ $$$$\:\:\:\:\:\:\:{Question}\::\:\:\:\:\:\:\mathrm{I}{f}\:\:\:{a}\:,\:{b}\:,\:{c}\:\:\in\:\mathbb{N}\:\:\:;\:{then}\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}!\ast{b}!\ast{c}!\mid\left({a}+{b}+{c}\right)!\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}\:.\:{july}\:\mathrm{970}# \\ $$

Question Number 112606 Answers: 1 Comments: 1

Question Number 112583 Answers: 1 Comments: 3

Question Number 112579 Answers: 4 Comments: 0

.... calculus .... Please Evaluate ::: Ω = ∫_0 ^(π/2) ((x/(sin(x))))^2 dx =??? M.N.july 1970#

$$\:\:\:\:\:\:\:\:....\:{calculus}\:.... \\ $$$$\mathscr{P}{lease}\:\:\mathscr{E}{valuate}\:::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left(\frac{{x}}{{sin}\left({x}\right)}\right)^{\mathrm{2}} {dx}\:=???\:\:\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathscr{M}.\mathscr{N}.{july}\:\mathrm{1970}# \\ $$$$\: \\ $$

Question Number 112576 Answers: 2 Comments: 1

Question Number 112575 Answers: 1 Comments: 0

Question Number 112572 Answers: 1 Comments: 1

Pg 1043 Pg 1044 Pg 1045 Pg 1046 Pg 1047 Pg 1048 Pg 1049 Pg 1050 Pg 1051 Pg 1052

Contact: info@tinkutara.com