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Question Number 107818 Answers: 2 Comments: 3

Question Number 107812 Answers: 2 Comments: 0

If the roots of the equation x^2 − x − 1 = 0 are α and β, provided that x_n = α^n + β^n . Find x_(16) .

$$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\:\:\mathrm{x}^{\mathrm{2}} \:\:−\:\:\mathrm{x}\:\:−\:\:\mathrm{1}\:\:\:=\:\:\mathrm{0}\:\:\:\mathrm{are}\:\:\:\alpha\:\:\mathrm{and}\:\:\beta, \\ $$$$\mathrm{provided}\:\mathrm{that}\:\:\:\:\:\:\mathrm{x}_{\mathrm{n}} \:\:=\:\:\alpha^{\mathrm{n}} \:\:+\:\:\beta^{\mathrm{n}} \:\:.\:\:\:\mathrm{Find}\:\:\:\:\mathrm{x}_{\mathrm{16}} . \\ $$

Question Number 107810 Answers: 1 Comments: 0

Question Number 107794 Answers: 2 Comments: 0

Question Number 107790 Answers: 4 Comments: 5

∫_0 ^1 ln(1+x^2 )dx

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

Question Number 107783 Answers: 0 Comments: 1

Σ_(n=1) ^∞ (1/(n2^n ))

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}\mathrm{2}^{{n}} } \\ $$

Question Number 107779 Answers: 1 Comments: 3

Question Number 107766 Answers: 4 Comments: 0

Question Number 107764 Answers: 0 Comments: 1

tanθ = ((Σ F_y )/(Σ F_x ))

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{tan}\theta\:=\:\:\frac{\Sigma\:\mathrm{F}_{\mathrm{y}} }{\Sigma\:\mathrm{F}_{\mathrm{x}} } \\ $$$$ \\ $$

Question Number 107756 Answers: 2 Comments: 0

((BeMath)/∐) ∫ x^2 ln (x^2 +3) dx

$$\:\frac{\mathcal{B}{e}\mathcal{M}{ath}}{\coprod} \\ $$$$\:\int\:{x}^{\mathrm{2}} \:\mathrm{ln}\:\left({x}^{\mathrm{2}} +\mathrm{3}\right)\:{dx}\: \\ $$

Question Number 107747 Answers: 3 Comments: 0

L=lim_(x→0) (((1−cos xcos 2xcos 3x)/(sin^2 2x))) = ?

$${L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}−\mathrm{cos}\:{x}\mathrm{cos}\:\mathrm{2}{x}\mathrm{cos}\:\mathrm{3}{x}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}{x}}\right)\:=\:? \\ $$

Question Number 107746 Answers: 1 Comments: 0

Question Number 107745 Answers: 2 Comments: 3

(i) L=lim_(x→0) [(((1+x)^(1/x) )/e)]^(1/x) = ? (ii) L=lim_(x→∞) [(x/e)−x((x/(x+1)))^x ] = ?

$$\left({i}\right)\:\:\:{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left[\frac{\left(\mathrm{1}+{x}\right)^{\mathrm{1}/{x}} }{{e}}\right]^{\mathrm{1}/{x}} \:\:=\:? \\ $$$$\left({ii}\right)\:\:{L}=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left[\frac{{x}}{{e}}−{x}\left(\frac{{x}}{{x}+\mathrm{1}}\right)^{{x}} \right]\:=\:? \\ $$

Question Number 107741 Answers: 0 Comments: 2

Question Number 107737 Answers: 1 Comments: 0

Question Number 107729 Answers: 6 Comments: 3

1) solve the D.E : (dy/dx)−y tan(x)=−y^2 sec(x) 2)find x Π_(k=1) ^(25) (x+(x/3^k ))=1 3)solve : ∣Z^2 ∣−4Z=0

$$\left.\mathrm{1}\right)\:{solve}\:{the}\:{D}.{E}\:\:\:: \\ $$$$\frac{{dy}}{{dx}}−{y}\:{tan}\left({x}\right)=−{y}^{\mathrm{2}} {sec}\left({x}\right)\: \\ $$$$ \\ $$$$\left.\mathrm{2}\right){find}\:{x} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\mathrm{25}} {\prod}}\left({x}+\frac{{x}}{\mathrm{3}^{{k}} }\right)=\mathrm{1} \\ $$$$ \\ $$$$\left.\mathrm{3}\right){solve}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mid{Z}^{\mathrm{2}} \mid−\mathrm{4}{Z}=\mathrm{0} \\ $$

Question Number 107728 Answers: 1 Comments: 0

Question Number 107727 Answers: 0 Comments: 0

Determine all possible solutions to the equation ; (1+t^3 )x′(t)+t^2 x(t)+t(x(t))^2 =0

$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions}\:\mathrm{to}\:\mathrm{the}\:\mathrm{equation}\:; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}+\mathrm{t}^{\mathrm{3}} \right){x}'\left(\mathrm{t}\right)+\mathrm{t}^{\mathrm{2}} {x}\left(\mathrm{t}\right)+\mathrm{t}\left({x}\left(\mathrm{t}\right)\right)^{\mathrm{2}} =\mathrm{0} \\ $$

Question Number 107718 Answers: 1 Comments: 0

Question Number 107714 Answers: 2 Comments: 0

((✓BeMath✓)/(cooll)) lim_(x→0) (1−tan x)^(4/(sin^2 x)) =?

$$\:\:\:\frac{\checkmark\mathcal{B}{e}\mathcal{M}{ath}\checkmark}{{cooll}} \\ $$$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{1}−\mathrm{tan}\:{x}\right)^{\frac{\mathrm{4}}{\mathrm{sin}\:^{\mathrm{2}} {x}}} \:=? \\ $$

Question Number 107711 Answers: 1 Comments: 1

Question Number 107710 Answers: 1 Comments: 0

✓((BeMath✓)/(cooll)) lim_(x→∞) (((x+5)/(x−3)))^((3x+1)/(cos 2x)) ?

$$\:\:\:\checkmark\frac{\mathcal{B}{e}\mathcal{M}{ath}\checkmark}{{cooll}} \\ $$$$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{x}+\mathrm{5}}{{x}−\mathrm{3}}\right)^{\frac{\mathrm{3}{x}+\mathrm{1}}{\mathrm{cos}\:\mathrm{2}{x}}} \:? \\ $$

Question Number 107706 Answers: 4 Comments: 0

✓BeMath✓ (1) ∫_0 ^∞ ((√x)/(1+x^3 )) dx ? (2) lim_(x→0) ((sin (π cos^2 x))/x^2 ) (3) If g(x)= 1+(√x) and (g○f)(x)=3+2(√x) +x find f(x)

$$\:\:\:\:\:\:\:\:\:\:\:\:\checkmark\mathcal{B}{e}\mathcal{M}{ath}\checkmark \\ $$$$\:\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{\sqrt{{x}}}{\mathrm{1}+{x}^{\mathrm{3}} }\:{dx}\:? \\ $$$$\:\:\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\pi\:\mathrm{cos}\:^{\mathrm{2}} {x}\right)}{{x}^{\mathrm{2}} }\: \\ $$$$\left(\mathrm{3}\right)\:{If}\:{g}\left({x}\right)=\:\mathrm{1}+\sqrt{{x}}\:{and}\:\left({g}\circ{f}\right)\left({x}\right)=\mathrm{3}+\mathrm{2}\sqrt{{x}}\:+{x} \\ $$$$\:\:\:{find}\:{f}\left({x}\right) \\ $$

Question Number 107704 Answers: 0 Comments: 0

Question Number 107705 Answers: 0 Comments: 0

Question Number 107696 Answers: 1 Comments: 1

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