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AllQuestion and Answers: Page 209

Question Number 200120 Answers: 1 Comments: 0

Question Number 200110 Answers: 1 Comments: 0

Question Number 200109 Answers: 1 Comments: 0

Question Number 200104 Answers: 0 Comments: 0

Question Number 200103 Answers: 1 Comments: 0

lim_(x→∞) sin (√(x+1))−sin (√x) =?

$$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{sin}\:\sqrt{\mathrm{x}+\mathrm{1}}−\mathrm{sin}\:\sqrt{\mathrm{x}}\:=? \\ $$

Question Number 200102 Answers: 1 Comments: 0

Question Number 200092 Answers: 1 Comments: 1

Question Number 200087 Answers: 1 Comments: 2

if ω ≠ 1 is a root of unity aand z is a complex number such that ∣z∣ = 1 then ∣((2+3ω+4zω^2 )/(4ω+3ω^2 z+2z))∣= ?

$$\:\:\mathrm{if}\:\omega\:\neq\:\mathrm{1}\:\mathrm{is}\:\mathrm{a}\:\mathrm{root}\:\mathrm{of}\:\mathrm{unity}\:\mathrm{aand}\:\mathrm{z}\:\mathrm{is}\:\mathrm{a}\: \\ $$$$\mathrm{complex}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that}\:\mid{z}\mid\:=\:\mathrm{1}\:\mathrm{then} \\ $$$$\:\:\mid\frac{\mathrm{2}+\mathrm{3}\omega+\mathrm{4}{z}\omega^{\mathrm{2}} }{\mathrm{4}\omega+\mathrm{3}\omega^{\mathrm{2}} {z}+\mathrm{2}{z}}\mid=\:? \\ $$

Question Number 200085 Answers: 1 Comments: 2

perimetre of White triangle?

$$\mathrm{perimetre}\:\mathrm{of}\:\:\mathrm{White}\:\mathrm{triangle}? \\ $$

Question Number 200105 Answers: 1 Comments: 2

Question Number 200075 Answers: 1 Comments: 0

Question Number 200066 Answers: 1 Comments: 0

If ((1 + x)/( (√3))) = 3 find x + (1/x) − 1 = ?

$$\mathrm{If}\:\:\:\frac{\mathrm{1}\:+\:\mathrm{x}}{\:\sqrt{\mathrm{3}}}\:=\:\mathrm{3}\:\:\:\mathrm{find}\:\:\:\mathrm{x}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\:−\:\mathrm{1}\:=\:? \\ $$

Question Number 200051 Answers: 2 Comments: 2

There are many ways to arrange 3 red balls and 9 black balls in a circle so that there are a minimum of 2 black balls between 2 adjacent red balls. (a) 180×8! (b) 240×7! (c) 364×6! (d) 282×4! (e) 144×5!

$$ \\ $$$$\mathrm{There}\:\mathrm{are}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{to}\:\mathrm{arrange}\:\mathrm{3}\:\mathrm{red} \\ $$$$\:\mathrm{balls}\:\mathrm{and}\:\mathrm{9}\:\mathrm{black}\:\mathrm{balls}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\: \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{a}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{2} \\ $$$$\mathrm{black}\:\mathrm{balls}\:\mathrm{between}\:\mathrm{2}\:\mathrm{adjacent}\:\mathrm{red} \\ $$$$\mathrm{balls}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{180}×\mathrm{8}!\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{240}×\mathrm{7}!\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{364}×\mathrm{6}! \\ $$$$\:\left(\mathrm{d}\right)\:\mathrm{282}×\mathrm{4}!\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{144}×\mathrm{5}!\: \\ $$

Question Number 200048 Answers: 0 Comments: 2

Question Number 200041 Answers: 3 Comments: 0

By strong induction prove that any natural number equal to or bigger than 8 can be written as 3a+5b where a and b are non−negative integers.

$${By}\:{strong}\:{induction}\:{prove}\:{that}\:{any} \\ $$$${natural}\:{number}\:{equal}\:{to}\:{or}\:{bigger}\:{than} \\ $$$$\mathrm{8}\:{can}\:{be}\:{written}\:{as}\:\mathrm{3}{a}+\mathrm{5}{b}\:{where}\:{a}\:{and}\:{b} \\ $$$${are}\:{non}−{negative}\:{integers}. \\ $$

Question Number 200040 Answers: 2 Comments: 0

Q: If , tan((π/4) −α )= (1/2) ⇒Find the value of , tan(4α)=?

$$ \\ $$$$\:\:\:\:\:{Q}:\:\:{If}\:\:,\:\:{tan}\left(\frac{\pi}{\mathrm{4}}\:−\alpha\:\right)=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\Rightarrow{Find}\:{the}\:{value}\:{of}\:,\:{tan}\left(\mathrm{4}\alpha\right)=? \\ $$$$ \\ $$

Question Number 200035 Answers: 1 Comments: 2

Question Number 200025 Answers: 3 Comments: 0

Question Number 200022 Answers: 0 Comments: 0

solve the associated legendre equation λ=l (l+1)η^2 ;l=0,1,2... and m^2 ≤ l(l+1) which requires −l≤m≤l using power series

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{associated}\:\mathrm{legendre}\:\mathrm{equation} \\ $$$$\lambda={l}\:\left({l}+\mathrm{1}\right)\eta^{\mathrm{2}} \:;{l}=\mathrm{0},\mathrm{1},\mathrm{2}...\:\:\:{and}\:{m}^{\mathrm{2}} \leqslant\:{l}\left({l}+\mathrm{1}\right)\: \\ $$$${which}\:{requires}\:−{l}\leqslant{m}\leqslant{l}\:\mathrm{using}\:\mathrm{power}\:\mathrm{series} \\ $$

Question Number 200019 Answers: 1 Comments: 0

Question Number 200013 Answers: 0 Comments: 3

Question Number 200012 Answers: 0 Comments: 0

Question Number 200053 Answers: 0 Comments: 1

Question Number 200061 Answers: 1 Comments: 0

∫_(−∞) ^(+∞) ((xsinx )/((x^2 +1)(x^2 +4)))dx = ??

$$\:\:\:\:\int_{−\infty} ^{+\infty} \frac{{x}\mathrm{sin}{x}\:}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{4}\right)}{dx}\:\:=\:\:\:?? \\ $$

Question Number 200060 Answers: 2 Comments: 0

Question Number 200005 Answers: 3 Comments: 0

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