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AllQuestion and Answers: Page 1211

Question Number 87088    Answers: 1   Comments: 0

Question Number 87086    Answers: 1   Comments: 0

Question Number 87074    Answers: 1   Comments: 4

what is coefficient of t^3 in the expanssion {((1−t^6 )/(1−t))}^3

$$\mathrm{what}\:\mathrm{is}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{t}^{\mathrm{3}} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expanssion}\:\left\{\frac{\mathrm{1}−\mathrm{t}^{\mathrm{6}} }{\mathrm{1}−\mathrm{t}}\right\}^{\mathrm{3}} \: \\ $$

Question Number 87069    Answers: 0   Comments: 1

((cos x−sin x)/(√(1+sin 2x))) = sec 2x−tan 2x prove it

$$\frac{\mathrm{cos}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}}{\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{2x}}}\:=\:\mathrm{sec}\:\mathrm{2x}−\mathrm{tan}\:\mathrm{2x} \\ $$$$\mathrm{prove}\:\mathrm{it}\: \\ $$

Question Number 87065    Answers: 0   Comments: 2

Question Number 87061    Answers: 1   Comments: 2

lim_(x→0) ((cos^3 (2x)−cos (x))/(cos^2 (2x)−cos (x))) =

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

Question Number 87059    Answers: 1   Comments: 0

(y ′)^2 −xy′ +y = 0 find the solution

$$\left(\mathrm{y}\:'\right)^{\mathrm{2}} −\mathrm{xy}'\:+\mathrm{y}\:=\:\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution} \\ $$

Question Number 87052    Answers: 0   Comments: 4

f(x)=∫_0 ^(π/2) ((sin^2 (t))/(1+xsin^2 (t)))dt

$${f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{{sin}^{\mathrm{2}} \left({t}\right)}{\mathrm{1}+{xsin}^{\mathrm{2}} \left({t}\right)}{dt} \\ $$

Question Number 87050    Answers: 0   Comments: 3

what are the roots of the system of equation (x/y)+(y/(x+1)) = (4/3) and x+y + xy = 5 ?

$$\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{system}\:\mathrm{of}\:\mathrm{equation}\:\frac{\mathrm{x}}{\mathrm{y}}+\frac{\mathrm{y}}{\mathrm{x}+\mathrm{1}}\:=\:\frac{\mathrm{4}}{\mathrm{3}} \\ $$$$\mathrm{and}\:\mathrm{x}+\mathrm{y}\:+\:\mathrm{xy}\:=\:\mathrm{5}\:? \\ $$

Question Number 87046    Answers: 1   Comments: 0

∫(dx/(sin^3 x+cos^3 x))

$$\int\frac{{dx}}{{sin}^{\mathrm{3}} {x}+{cos}^{\mathrm{3}} {x}} \\ $$

Question Number 87034    Answers: 1   Comments: 0

A and B are running along the wall of a square park. The corners of the park are facing north, south, east and west and are named N, S, E, W respectively. They start at E and run towards S. If the speed of A is 6 tines that of B, where do they meet for the 27^(th) time?

$$\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{running}\:\mathrm{along}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{square}\:\mathrm{park}.\:\mathrm{The}\:\mathrm{corners}\:\mathrm{of}\:\mathrm{the}\:\mathrm{park} \\ $$$$\mathrm{are}\:\mathrm{facing}\:\mathrm{north},\:\mathrm{south},\:\mathrm{east}\:\mathrm{and}\:\mathrm{west} \\ $$$$\mathrm{and}\:\mathrm{are}\:\mathrm{named}\:\mathrm{N},\:\mathrm{S},\:\mathrm{E},\:\mathrm{W}\:\:\mathrm{respectively}. \\ $$$$\mathrm{They}\:\mathrm{start}\:\mathrm{at}\:\mathrm{E}\:\mathrm{and}\:\mathrm{run}\:\mathrm{towards}\:\mathrm{S}.\:\mathrm{If} \\ $$$$\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{A}\:\mathrm{is}\:\mathrm{6}\:\mathrm{tines}\:\mathrm{that}\:\mathrm{of}\:\mathrm{B},\:\mathrm{where} \\ $$$$\mathrm{do}\:\mathrm{they}\:\mathrm{meet}\:\mathrm{for}\:\mathrm{the}\:\mathrm{27}^{\mathrm{th}} \:\mathrm{time}? \\ $$

Question Number 87048    Answers: 0   Comments: 0

Express into partial fractions (x^6 /(x^(12) +1))

$${Express}\:\:{into}\:\:{partial}\:\:{fractions} \\ $$$$\:\:\:\:\:\:\:\:\frac{{x}^{\mathrm{6}} }{{x}^{\mathrm{12}} +\mathrm{1}} \\ $$

Question Number 87031    Answers: 1   Comments: 1

Question Number 87033    Answers: 1   Comments: 0

Find the value of x^3 + (1/x^3 ) , when x + (1/x) = 5

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}^{\mathrm{3}} +\:\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\:\:\:,\:\:\:\mathrm{when} \\ $$$$\:\:\:{x}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{5} \\ $$

Question Number 87028    Answers: 0   Comments: 0

solve D.E (dy/dx)+((ysec^3 y)/x)=x^2 y^2

$${solve}\:{D}.{E} \\ $$$$\frac{{dy}}{{dx}}+\frac{{y}\mathrm{sec}\:^{\mathrm{3}} {y}}{{x}}={x}^{\mathrm{2}} {y}^{\mathrm{2}} \\ $$

Question Number 87027    Answers: 1   Comments: 0

Question Number 87025    Answers: 0   Comments: 2

∫_0 ^(π/2) ((arc tan ((√2) tan x))/(tan x)) dx?

$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{arc}\:\mathrm{tan}\:\left(\sqrt{\mathrm{2}}\:\mathrm{tan}\:\mathrm{x}\right)}{\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}?\: \\ $$

Question Number 87023    Answers: 0   Comments: 1

∫ (dx/(√(x^2 −8x+15))) ?

$$\int\:\:\frac{\mathrm{dx}}{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{8x}+\mathrm{15}}}\:?\: \\ $$

Question Number 87021    Answers: 0   Comments: 0

∫((ln(1+asin(x^2 ))/(sin(x^2 )))dx

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

Question Number 87014    Answers: 1   Comments: 1

calculate ∫_0 ^∞ (e^(−[2x]) /((x+1)^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−\left[\mathrm{2}{x}\right]} }{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 87013    Answers: 0   Comments: 2

calculate ∫_0 ^∞ (e^(−[x]) /(x+1))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−\left[{x}\right]} }{{x}+\mathrm{1}}{dx} \\ $$

Question Number 87009    Answers: 2   Comments: 0

solve 7⌊x+3⌋^2 −3⌊x⌋+6=5 mod 11

$${solve} \\ $$$$\mathrm{7}\lfloor{x}+\mathrm{3}\rfloor^{\mathrm{2}} −\mathrm{3}\lfloor{x}\rfloor+\mathrm{6}=\mathrm{5}\:{mod}\:\mathrm{11} \\ $$

Question Number 86998    Answers: 1   Comments: 0

∫((6e^x )/(e^(2x) −1)) dx

$$\int\frac{\mathrm{6}{e}^{{x}} }{{e}^{\mathrm{2}{x}} −\mathrm{1}}\:{dx} \\ $$

Question Number 86995    Answers: 1   Comments: 0

∫_0 ^π ((a^n sin^2 (x)+b^n cos^2 (x))/(a^(2n) sin^2 (x)+b^(2n) cos^2 (x)))dx ; a>b

$$\int_{\mathrm{0}} ^{\pi} \frac{{a}^{{n}} {sin}^{\mathrm{2}} \left({x}\right)+{b}^{{n}} {cos}^{\mathrm{2}} \left({x}\right)}{{a}^{\mathrm{2}{n}} {sin}^{\mathrm{2}} \left({x}\right)+{b}^{\mathrm{2}{n}} {cos}^{\mathrm{2}} \left({x}\right)}{dx}\:;\:{a}>{b} \\ $$

Question Number 86994    Answers: 0   Comments: 0

Question Number 86993    Answers: 1   Comments: 1

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