The cissoids r = a sin 0 tan 0. (See Exercise 29.) Ans. sin 0 cos 0 dr - r(1 + cos? 0) de = 0. %3D

Q: sin(e)de 4+cos (e) In(4+cos'(e)) +c -sinh -sinh cos (0) sinh (cos (0)) +c 2/4+cos (0)

A: Use the substitution method and integrate the given expression.

Q: Find the area inside the circle r=−3acosθ and outside the cardioid r=a(1−cosθ), a>0

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Q: With the hints of using the relationship sin?(r) + cos²(r) = 1 and choosing 1= sin(r) integrate cos…

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Q: az If r?sin(0) = (rcos(0) – 1)z , where r and 0 are independent, determine az and ae D. ar…

A: Given: r2sinθ=rcosθ-1z We have to find ∂z∂r and ∂z∂θ. Partial differentiation: Differentiation of a…

Q: a) Show, from 1st principles, that if a small angle x is measured in radian, then: i) ii) sin x = x…

A: take a triangle as below :

Q: . The area of the region that lies inside the cardioid curve r = cos 0 + 1 and outside the circle r…

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Q: H.W: 1. Find the area of the region inside the oval limacon r = 4 +2 cos 0 2. Find the area of the…

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Q: A particle is moving with the given data. Find the position of the particle. cos(t)sin(t), s(0) 1,…

A: It is given that

Q: The region inside the circle r = /2 sin 0 and inside the lemniscate r? = sin 20. Which of the…

A: here option (a) is true because on doing simplifying we get r=2sin^2theeta and limit will be o to…

Q: Determine the concavity and find the poir (a) y = 2 cos x + sin 2x, 0 < x < 2T %3D

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Q: Find the area of the region shared by the cardioids r= 12(1+ cos 0) and r= 12(1- cos 0). The area…

A: General equation of the cardioids is r=a(1+cosθ) and Area of the cardioids is 6πa2

Q: The area which is inside the circle r = 8 cos 0 and outside the circle r = 2 cos 0. %3D

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Q: After choosing the appropriate trigonometric substitution the integral| /4 dx, becomes cot2 tan tan?…

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Q: The area of the region inside the circle r= 6 cos e and outside the cardioid r= 2(1+ cos 6), a > 0…

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Q: Eliminate 0 from the equations : (i) x = h + a cos 0, y = k + b sin 0 (ii) x = a ser³ 0, y = b cot³…

A: Solution is given: Hope the solution is helpful.

Q: sin a =2 and cosec a = Cos a = and sec a = %3D tan a = and cot a = = %3D LIA た一〇

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Q: Determine the value of C in on the antiderivative of F(x) = sin°(x)cos“(x) for x = 0.083 and y =…

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Q: If sin(x +y) = xy, what is the correct expression for -? dx cos(x + y) – y (A х-1 cos(x + y) – y (B…

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Q: The area of the region in the second quadrant that is within r=2+2 Sin e Зл None -1 2 Зл +4 2

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Q: sin? 0 2) cos 0 = sec 0- cos e %3D

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Q: Carrying out a trigonometric substitution on the integral x2- 4 dx. 25 „it is obtained that it is…

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Q: /9- x² Consider dy using Trigonometric Substitution what is dx ? 3 sec e de 3 sec? e de 3 cos e de 3…

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Q: After choosing the appropriate trigonometric substitution the integral x2 -dx, becomes 4 sin (0)de S…

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Q: The arc length of the graph of y = In(cos æ) from the point where a = 0 to the point where a I is…

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Q: (c) f(x) = sin? x [Hint: sin? r = l-cos 21] (a) f(r) = r arctan r b) f(x)=x²e- %3D

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Q: a (t) = 3 cos t – 2 sin t, s (0) = 0, v(0) = 4 -

A: Proceed as shown below...

Q: A particle is moving with the given data. Find the position of the particle, s(t). a(t) = 7 cos(t) −…

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Q: After choosing the appropriate trigonometric substitution the integral - dx, becomes None tan? (0)d0…

A: Given:integral is ∫4-x2x2dxso if we know that sin2θ+cos2θ=1if we substitute 2sinθ in the place of…

Q: 11) Define A(k) = x dx Using area, create a nice formula for A(k). Explain your area reasoning.…

A: As per bartleby guidelines we are supposed to answer only 3 sub parts of a question. This question…

Q: Determine the value of C in on the antiderivative of F(x) = sin³(x)cosª(x) for x = 0.435 and y =…

A: Antiderivative of F(x)=cos4(x) sin3(x) isy=∫cos4(x) sin3(x) dx

Q: The area between the two loops of the limacon r = 1 + 2 sin 0.

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Q: Cos A +1+ sin A 2 sec A 1+ sin A %3D cos A

A: To Prove: cosA1+sinA+1+sinAcosA=2secA

Q: 3. K. 16 • sin L = sin M = 34 • cos L = • cos M = %3D • tan L = • tan M = %3D M O Gina Wison (All…

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Q: cos? e + cose +1 = 0 [0,2m]

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Q: A particle is moving with the given data. Find the position of the particle. a(t) = 11 sin(t) + 7…

A: Find the position of the particle.

Q: sin" e de, (b) Given that In %3D Show that forn 2 2, n- In-2 %3D Hence, evaluate I5.

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Q: Determine the value of C in on the antiderivative of F(x) = sin°X)cos"(x) for x = 0.579 and y = 1.3.…

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Q: For which value of a is the length of the cardioid r = a(1+ sin 0), 0 < 0 < 2ñ _32 units? 6 2 -4 -2

A: Solution

Q: (a) sin a = %3D (b) cos a = (c) csc a = (d) sec a = (e) cot a =

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Q: s).F ecosa sin a da cos a sin a da 2

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Q: Find the area of the shaded region. r = 44 cos 0 r = 44/3 sin 0 NOTE: Enter the exact answer.

A: Use polar coordinates

Q: 10. By trigonometric substitution, we can transform dx into x*V4 - x2 A. Ssi'e sin ede В. 1 1 С. 32J…

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Q: Given f(x,y,z) = cos(5xy) + decimal places. sin(4z). Find f, (6,6,0). Leave your answer correct to…

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Q: The area between the two loops of the limacon r = 1+2 sin 0.

A: Question- The area between the two loops of the limacon          r = 1 + 2  sin theta .

Q: Cos (a). g + sin (&) = %3D sin(a) =4 (The aPpro Priate a ssigh ment) .: Hint %3D

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Q: 4. The teardrop x = 2a cos t – a sin 2t, y = b sin t, 0 < t < 27 find area y 2a

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Q: Find the area of the region shared by the cardioids r= 4(1 + cos 0) and r= 4(1 – cos 0). The area…

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Q: Answer the question below: Let h(x, y, z) = ze*y + x² cos(z) cot(y³). The student should find hyzx.

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