Evaluate the following double integral a) Evaluate 8xy dxdy=? 1 b) Evaluate the following integral by using the polar coordinates

Q: Evaluate the integral sec? r Vtan3 x dx. (a) tan x + C 2 (c) = tanš x + C (b) ; tan? r + C 2 (d) =…

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A: Given lines are, x=8t+2,y=3,z=-t+1And x=2s+2, y=2s+3, z=s+1⇒x-28=y-30=z-1-1=t…

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A: We know that equation of line passing through the point (x1 ,y1) and having slope m is,…

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A: Here we have to integrate the given Integral.

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Q: 4. y = sec-1 Activities in Inverse Trigonometric Functions dy Find the dx 1. y = sin-12x – V1– 4x²…

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Q: 1. Find the maximum value of the function f(x.y)= 4x + 2y +x* - 2x*+ 2xy– 3y° on the interval –2 to…

A: Note: Only part b) comes under calculus. Part a) and part c) are not covered under calculus. Hence,…

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Q: Provide a step-by-step solution to the following differential equation (linear quation) y' = x3 -…

A: I am attaching image so that you understand each and every step.

Q: 2-fx'e-2x* dx

A: To evaluate: I=∫x3e-2x4dx Substituting x4=u⇒4x3dx=du⇒x3dx=du4

Q: Describe the graph of the equation. r = 6 sin 9t i – 6 cos 9t j O Itis a circle of radius 6 in the…

A: Given curve  r= 6sin(9t)i-6cos(9t)j =xi+yj So, x=6sin(9t) , y= -6cos(9t)

Q: 4) A particle is moving along the curve y = vx. As the particle passes through the point (4,2), its…

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Q: Question 1 Use the First Derivative Test to find the local maximum and minimum values of the…

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Q: dy 5. S: y(1-Vy)2

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Q: Consider the differential equation y" – - 1ly" + 28y = 0 %3D

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Q: QI: Solve the following DE: e*dx-ydy 0y(0) = 1

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: The region is bounded by y=9-2x from y=0 to y=8 and x=0

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Q: Question

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Q: tan x d. y = sec? t dt 3 е. y = dx 1— х2. its

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Q: 6. A square plate 3 ft on each side is submerged with the top side parallel to the surface, 5 ft…

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Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (7t + 6)i + tj, 0st<1

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Q: Question 8 of 10 v(x) = 4 cos(sin(3x)) Select the correct response: - 12 sin(3.r) cos²(3x) cos²(3.r)…

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Q: Use l'Hôpital's Rule to evaluate lim 4x( cos (2x) - 1) sin (5x) - 5x 4x( cos (2x) - 1) lim sin (5x)…

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Q: We have 1 d (In(x² + 1)) : dx x2 + 1 Select one: O True O False

A: As we know that; The Chain rule; fgx'=f'gx·g'x The Power law; ddxxn=nxn-1 And ddxlnx=1x   Given;…

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Q: Carlo works in a restaurant and makes S6 per hour plus tips. He is receiving an average of $5 per…

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Q: . A cylindrical tank full of water has a radius 2 ft and a height of 6 ft. Find the work m pumping…

A: Work = force × distance Force = weight

Q: 1. f'(x)dx if f(2) = 1 2. f(x) = S(x² + x – 3)dx if f (2) = 3 3. f(x) = S xe*dx if f(2) = 3 4. f(x)…

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Q: 1. S 7e*dx 2. S(5e* 6*)dx 3. § 3(5*)dx

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Verify Green's Theorem by evaluating both integrals v dx + x* dy = // aN ƏM dA ду əx for the given…

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Q: b. = log(a + b) a If log + log- %3D a then we can conclude that O a. a-b-1 O b. a?-b2 =1 O C. a+b=1…

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Q: Compute for the initial velocity of 3÷(cos(45)×38. Show your complete solution

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Q: Find the arc length of the parametric curve. = 4 cos(t), y = 4 sin(t), % = 3t; 0 < t < T L =

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Q: tan 0 =-1, 0 in QIV

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Q: Sketch the region and find the area of the region bounded by y = -x2 + 9 and the x-axis.

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Q: 3. Determine the differential coefficient of y =-+2x – 3 when x = 7 4. If f(t) = 3 sin(4t + 0.12) –…

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