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Question Number 30425 Answers: 1 Comments: 0

decompose inside R[x] F(x)= (x^(2n) /((x^2 +1)^n )) with n from N and n>0.

$${decompose}\:{inside}\:{R}\left[{x}\right]\: \\ $$$${F}\left({x}\right)=\:\:\:\frac{{x}^{\mathrm{2}{n}} }{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{{n}} }\:\:\:{with}\:{n}\:{from}\:{N}\:{and}\:{n}>\mathrm{0}. \\ $$

Question Number 30405 Answers: 1 Comments: 0

x^2 +y^2 =13 x^2 −3xy+y^2 =35 find the value of x and y

$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{13} \\ $$$${x}^{\mathrm{2}} −\mathrm{3}{xy}+{y}^{\mathrm{2}} =\mathrm{35} \\ $$$${find}\:{the}\:{value}\:{of}\:{x}\:{and}\:{y} \\ $$

Question Number 30401 Answers: 0 Comments: 0

is there exists a onto group homo from D4 to Z4?

$${is}\:{there}\:{exists}\:{a}\:{onto}\:{group}\:{homo}\:{from}\:{D}\mathrm{4}\:{to}\:{Z}\mathrm{4}? \\ $$

Question Number 30390 Answers: 0 Comments: 5

Question Number 30377 Answers: 1 Comments: 1

Question Number 30373 Answers: 0 Comments: 4

Question Number 30436 Answers: 1 Comments: 1

let ϕ(x)=1−2^(1−x) prove that ϕ(x)=(x−1)ln2 −(((ln2)^2 )/2)(x−1)^2 +o((x−1)^2 ).

$${let}\:\varphi\left({x}\right)=\mathrm{1}−\mathrm{2}^{\mathrm{1}−{x}} \:\:{prove}\:{that} \\ $$$$\varphi\left({x}\right)=\left({x}−\mathrm{1}\right){ln}\mathrm{2}\:−\frac{\left({ln}\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{2}}\left({x}−\mathrm{1}\right)^{\mathrm{2}} \:+{o}\left(\left({x}−\mathrm{1}\right)^{\mathrm{2}} \right). \\ $$

Question Number 30367 Answers: 0 Comments: 7

Question Number 30366 Answers: 0 Comments: 1

Question Number 30364 Answers: 1 Comments: 2

Question Number 30356 Answers: 1 Comments: 0

If sin 2θ= cos 3θ and θ is an acute angle, then sin θ equals

$$\mathrm{If}\:\mathrm{sin}\:\mathrm{2}\theta=\:\mathrm{cos}\:\mathrm{3}\theta\:\:\mathrm{and}\:\theta\:\mathrm{is}\:\mathrm{an}\:\mathrm{acute} \\ $$$$\mathrm{angle},\:\mathrm{then}\:\mathrm{sin}\:\theta\:\mathrm{equals} \\ $$

Question Number 30355 Answers: 2 Comments: 0

Question Number 30354 Answers: 1 Comments: 0

If g(x)=∫_0 ^x cos^4 t dt, then g (x+π) =

$$\mathrm{If}\:\:{g}\left({x}\right)=\overset{{x}} {\int}_{\mathrm{0}} \mathrm{cos}^{\mathrm{4}} {t}\:{dt},\:\mathrm{then}\:{g}\:\left({x}+\pi\right)\:= \\ $$

Question Number 30350 Answers: 1 Comments: 0

Question Number 30331 Answers: 2 Comments: 0

Question Number 30340 Answers: 1 Comments: 0

Question Number 30321 Answers: 0 Comments: 3

∫_(−∞) ^∞ (e^(ax) /(e^x +1))dx=?

$$\int_{−\infty} ^{\infty} \frac{\mathrm{e}^{\mathrm{a}{x}} }{\mathrm{e}^{{x}} +\mathrm{1}}{dx}=? \\ $$

Question Number 30323 Answers: 0 Comments: 0

Question Number 30299 Answers: 1 Comments: 5

Question Number 30282 Answers: 0 Comments: 3

Find lim_(n→∞) cos^n (((2π)/n))

$${Find}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}cos}^{{n}} \:\left(\frac{\mathrm{2}\pi}{{n}}\right) \\ $$

Question Number 30348 Answers: 0 Comments: 1

Question Number 30267 Answers: 0 Comments: 7

Can We expand the following expression? (1+x)(1+2x)(1+3x)......(1+nx) or is there any formula for this?

$${Can}\:{We}\:{expand}\:{the}\:{following} \\ $$$${expression}? \\ $$$$\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+\mathrm{2}{x}\right)\left(\mathrm{1}+\mathrm{3}{x}\right)......\left(\mathrm{1}+{nx}\right) \\ $$$${or}\:{is}\:{there}\:{any}\:{formula}\:{for}\:{this}? \\ $$

Question Number 30259 Answers: 1 Comments: 1

Question Number 30258 Answers: 2 Comments: 0

Question Number 30257 Answers: 1 Comments: 5

Question Number 30256 Answers: 0 Comments: 1

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