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AllQuestion and Answers: Page 1272

Question Number 87146 Answers: 1 Comments: 0

find the area of the region enclosed by the polar curve r = 4 + 2 cos θ ?

$$\mathrm{find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\: \\ $$$$\mathrm{enclosed}\:\mathrm{by}\:\mathrm{the}\:\mathrm{polar}\:\mathrm{curve}\: \\ $$$$\mathrm{r}\:=\:\mathrm{4}\:+\:\mathrm{2}\:\mathrm{cos}\:\theta\:? \\ $$

Question Number 87133 Answers: 0 Comments: 2

Question Number 87130 Answers: 0 Comments: 5

find the slope for the curve r = 3 sin 2θ at θ =(π/4) ?

$$\mathrm{find}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{for}\:\mathrm{the}\:\mathrm{curve}\: \\ $$$$\mathrm{r}\:=\:\mathrm{3}\:\mathrm{sin}\:\mathrm{2}\theta\:\mathrm{at}\:\theta\:=\frac{\pi}{\mathrm{4}}\:? \\ $$

Question Number 87125 Answers: 0 Comments: 3

Question Number 87121 Answers: 3 Comments: 0

∫_0 ^(π/2) ((1−x^4 )/(1+x^4 ))dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}−{x}^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 87116 Answers: 1 Comments: 0

(d^2 y/dx^2 )+x^2 y=0

$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+{x}^{\mathrm{2}} {y}=\mathrm{0} \\ $$

Question Number 87105 Answers: 2 Comments: 1

Question Number 87103 Answers: 2 Comments: 2

∫(dx/((1+x)(√(x−x^2 ))))

$$\int\frac{{dx}}{\left(\mathrm{1}+{x}\right)\sqrt{{x}−{x}^{\mathrm{2}} }} \\ $$

Question Number 87093 Answers: 0 Comments: 6

⌊((x−1)/4)⌋+⌊((x−2)/3)⌋=⌊((x−3)/2)⌋

$$\lfloor\frac{{x}−\mathrm{1}}{\mathrm{4}}\rfloor+\lfloor\frac{{x}−\mathrm{2}}{\mathrm{3}}\rfloor=\lfloor\frac{{x}−\mathrm{3}}{\mathrm{2}}\rfloor \\ $$

Question Number 87089 Answers: 0 Comments: 5

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

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