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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

Question Number 112573 Answers: 1 Comments: 0

Question Number 112542 Answers: 1 Comments: 0

If 7 sin y = 8 sin (y+45°). find the value of tan (y+45°) ?

$$\mathrm{If}\:\mathrm{7}\:\mathrm{sin}\:\mathrm{y}\:=\:\mathrm{8}\:\mathrm{sin}\:\left(\mathrm{y}+\mathrm{45}°\right).\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:\left(\mathrm{y}+\mathrm{45}°\right)\:? \\ $$

Question Number 112538 Answers: 1 Comments: 0

Question Number 112528 Answers: 0 Comments: 2

If ((n−7)/(n−17)) and ((n−14)/(n−24)) are integers numbers n=?

$${If}\:\:\:\:\:\frac{{n}−\mathrm{7}}{{n}−\mathrm{17}}\:\:\:\:\:\:\:{and}\:\:\:\:\frac{{n}−\mathrm{14}}{{n}−\mathrm{24}}\:\:\:{are}\:{integers}\:{numbers} \\ $$$${n}=? \\ $$

Question Number 112522 Answers: 0 Comments: 0

prove that ∫_0 ^1 ((x^2 ln^2 (x))/(1−x^4 ))dx=(7/8)ζ(3)−(π^3 /(32))

$${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{2}} \mathrm{ln}^{\mathrm{2}} \left({x}\right)}{\mathrm{1}−{x}^{\mathrm{4}} }{dx}=\frac{\mathrm{7}}{\mathrm{8}}\zeta\left(\mathrm{3}\right)−\frac{\pi^{\mathrm{3}} }{\mathrm{32}} \\ $$

Question Number 112521 Answers: 0 Comments: 3

2^x =4x

$$\mathrm{2}^{\mathrm{x}} =\mathrm{4x}\:\:\:\:\:\: \\ $$

Question Number 112520 Answers: 0 Comments: 0

∫(((cos(x)))^(1/3) /(cos(x)))dx

$$\int\frac{\sqrt[{\mathrm{3}}]{{cos}\left({x}\right)}}{{cos}\left({x}\right)}{dx} \\ $$

Question Number 112509 Answers: 0 Comments: 1

Question Number 112507 Answers: 1 Comments: 0

Question Number 112506 Answers: 0 Comments: 0

Question Number 112505 Answers: 1 Comments: 0

Given matrix A= (((1 0)),((2 3)) ) , B= (((−1 −3)),(( 2 0)) ) and AX +2B = I . what the value of det (X) ?

$$\mathrm{Given}\:\mathrm{matrix}\:\mathrm{A}=\begin{pmatrix}{\mathrm{1}\:\:\:\:\mathrm{0}}\\{\mathrm{2}\:\:\:\mathrm{3}}\end{pmatrix}\:,\:\mathrm{B}=\begin{pmatrix}{−\mathrm{1}\:\:\:\:\:−\mathrm{3}}\\{\:\:\:\mathrm{2}\:\:\:\:\:\:\:\:\:\mathrm{0}}\end{pmatrix} \\ $$$$\mathrm{and}\:\mathrm{AX}\:+\mathrm{2B}\:=\:\mathrm{I}\:.\:\mathrm{what}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{det}\:\left(\mathrm{X}\right)\:? \\ $$

Question Number 112503 Answers: 0 Comments: 0

Question Number 112502 Answers: 1 Comments: 0

Question Number 112501 Answers: 0 Comments: 0

Find the radius of convergent of the power series: Σ_(n = 1) ^∞ (((n + 2)/n))^n^2 x^n

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{convergent}\:\mathrm{of}\:\mathrm{the}\:\mathrm{power}\:\mathrm{series}:\:\:\:\underset{\mathrm{n}\:\:=\:\:\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{n}\:\:+\:\:\mathrm{2}}{\mathrm{n}}\right)^{\mathrm{n}^{\mathrm{2}} } \mathrm{x}^{\mathrm{n}} \\ $$

Question Number 112500 Answers: 1 Comments: 0

Question Number 112494 Answers: 2 Comments: 0

y(√(1+x^2 )) dx + x(√(1+y^2 )) dy = 0

$$\:\mathrm{y}\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:+\:\mathrm{x}\sqrt{\mathrm{1}+\mathrm{y}^{\mathrm{2}} }\:\mathrm{dy}\:=\:\mathrm{0} \\ $$

Question Number 112492 Answers: 1 Comments: 0

evaluate lim_(n→∞) Σ_(k=1) ^n (1/(n+k^2 ))

$${evaluate} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{n}+{k}^{\mathrm{2}} } \\ $$

Question Number 112498 Answers: 0 Comments: 0

∫((ln(1+x)dx)/((1+x^2 )))

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

Question Number 112497 Answers: 2 Comments: 0

If lim_(x→0) ((sin 2x + asin x)/x^3 ) exist what is the value of a and the limit?

$$\mathrm{If}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{2x}\:+\:\mathrm{asin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{3}} }\:\mathrm{exist}\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{the}\:\mathrm{limit}? \\ $$

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