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Question Number 38892 Answers: 1 Comments: 0

lim_(x→0) ((x(1+ a cos x)−b sin x)/x^5 )=1 find the value a and b

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\left(\mathrm{1}+\:{a}\:\mathrm{cos}\:{x}\right)−{b}\:\mathrm{sin}\:{x}}{{x}^{\mathrm{5}} }=\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:{a}\:\mathrm{and}\:{b} \\ $$

Question Number 38881 Answers: 1 Comments: 0

solve for 0 ≤ θ ≤π, the equations a)_ cos (2θ − (π/2))= (1/2) b) cos θ − (√3) sin θ = 0

$${solve}\:{for}\:\mathrm{0}\:\leqslant\:\theta\:\leqslant\pi,\:{the}\:{equations} \\ $$$$\left.{a}\right)_{} \:\mathrm{cos}\:\left(\mathrm{2}\theta\:−\:\frac{\pi}{\mathrm{2}}\right)=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left.{b}\right)\:\mathrm{cos}\:\theta\:−\:\sqrt{\mathrm{3}}\:{sin}\:\theta\:=\:\mathrm{0} \\ $$

Question Number 38880 Answers: 1 Comments: 0

Find the equation of the perpendicular bisector of the line segment joining the points (1,3) and (5,1)

$${Find}\:{the}\:{equation}\:{of}\:{the}\:{perpendicular} \\ $$$${bisector}\:{of}\:{the}\:{line}\:{segment}\:{joining} \\ $$$${the}\:{points}\:\left(\mathrm{1},\mathrm{3}\right)\:{and}\:\left(\mathrm{5},\mathrm{1}\right) \\ $$

Question Number 38879 Answers: 1 Comments: 0

Find the equation of the line through (2,−3) which make angles 45° with the line 2x − y = 2.

$${Find}\:{the}\:{equation}\:{of}\:{the}\:{line}\:{through} \\ $$$$\left(\mathrm{2},−\mathrm{3}\right)\:{which}\:{make}\:{angles}\:\mathrm{45}°\:{with} \\ $$$${the}\:{line}\:\mathrm{2}{x}\:−\:{y}\:=\:\mathrm{2}. \\ $$

Question Number 38878 Answers: 1 Comments: 0

Find the equation on a line joining the points A(2x,4),B(x,3) and C(4,3)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{on}\:\mathrm{a}\:\mathrm{line}\:\mathrm{joining} \\ $$$$\mathrm{the}\:\mathrm{points}\:\mathrm{A}\left(\mathrm{2}{x},\mathrm{4}\right),{B}\left({x},\mathrm{3}\right)\:{and}\: \\ $$$${C}\left(\mathrm{4},\mathrm{3}\right) \\ $$

Question Number 38924 Answers: 1 Comments: 0

A wave has a wavelength of 1.5m, calculate the phase angle between a point 0.25m from the peak of the wave and another point 1m further along the same peak.

$${A}\:{wave}\:{has}\:{a}\:{wavelength}\:{of}\:\mathrm{1}.\mathrm{5}{m}, \\ $$$${calculate}\:{the}\:{phase}\:{angle}\:{between} \\ $$$${a}\:{point}\:\mathrm{0}.\mathrm{25}{m}\:{from}\:{the}\:{peak}\:{of}\:{the} \\ $$$${wave}\:{and}\:{another}\:{point}\:\mathrm{1}{m}\:{further} \\ $$$${along}\:{the}\:{same}\:{peak}. \\ $$

Question Number 38876 Answers: 1 Comments: 2

solve: (d^2 y/dx^2 ) + 2x (dy/dx) + 5y = 0

$$\mathrm{solve}:\:\:\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:\:+\:\:\mathrm{2x}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:+\:\mathrm{5y}\:=\:\mathrm{0} \\ $$

Question Number 38870 Answers: 0 Comments: 0

i am posting what i think helpful...

$${i}\:{am}\:{posting}\:{what}\:{i}\:{think}\:{helpful}... \\ $$

Question Number 38865 Answers: 0 Comments: 0

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Question Number 39030 Answers: 2 Comments: 3

1) let f(x) = ∫_0 ^∞ (dt/(1+x^2 t^4 )) with x >0 find a simple form of f(x) 2) calculate ∫_0 ^(+∞) (dt/(1+t^4 )) 3) calculate ∫_0 ^∞ (dt/(1+3t^4 ))

$$\left.\mathrm{1}\right)\:{let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\mathrm{1}+{x}^{\mathrm{2}} {t}^{\mathrm{4}} }\:\:{with}\:{x}\:>\mathrm{0} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{4}} } \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dt}}{\mathrm{1}+\mathrm{3}{t}^{\mathrm{4}} } \\ $$

Question Number 38849 Answers: 1 Comments: 1

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Question Number 38836 Answers: 0 Comments: 0

Question Number 38825 Answers: 1 Comments: 4

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