Which derivative rule is used to derive the Integration by Parts formula? A. The Integration by Parts formula is derived from the Implicit Differentiation Rule. B. The Integration by Parts formula is derived from the Product Rule. C. The Integration by Parts formula is derived from the Chain Rule. D. The Integration by Parts formula is derived from the Power Rule.

Q: Find the Area of the Surface obtained by rotating the curve about the y y = √√x, 1 ≤ y ≤2

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Q: The gradient of the tangent to the curve y=-3x³ + 4ax² - 5x + 4 at x = 1 is 2. The value of a is 2.…

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Q: 1. A certain ellipse is centered at the origin from which the major axis is always equal to 25 and…

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Q: 6. Find the limit, if it exists. If the limit does not exist, explain why. tan 5x sin 6x (a) lim x-0…

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Q: 2r find the moment with respect to the wavic of the area hounded by the parabola v - Av-172 and v

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Q: 6. Find the limit, if it exists. If the limit does not exist, explain why. tan 5x sin 6x (a) lim 1-0…

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Q: Let line l : x=y/2=z/3 and point P(1,0,1). Find an equation of the plane (in point-normal form)…

A: Solution of given question is written in below steps.

Q: 18. What is the length of the polar curve below? 3πt x = 8cos (0) for 0 ≤ 0 ≤ ³1

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Q: Find the Area of the Surface obtained by rotating the curve about the x - axis X= (²+2),

A: The objective is to find the surface area.

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Q: vy B. Find the derivative of function f(x, y, z) = 3e* cosxy + ex² + Inzx at point P(1,0,) in the…

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Q: ND THE AREA BOUNDED BY THE = x(x-1)², y-AXIS, AND THE =12

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Q: 1) Find |R'(t)|, Make sure to simplify your answer 2) Find the distance traveled by a particle…

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Q: e2-s L-1 (5(5²-53) O [(-1/3) + e^(4(t-1))/3] e^2 U(t-1) O [(-1/3) + e^(3(t-1))/3] e^2 U(t-1) O None…

A: We have to find the inverse Laplace transform of the above expression.

Q: x-4 x²+2x-15 Inx+51-Inx-31+ C 8 Option 1 S: dx 1 (x + 5)⁹1 Je In + C + x-3 -100 1 9 In|x + 5|ln|x −…

A: We can find the answer as below

Q: Find the area bounded by the curves y-x² = -3,x+y = 3 and y = 0.5x.

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Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = 9y - y² and y =…

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Q: Find the exact length of the polar curve described by: r = 2e-0 on the interval 7 6" π ≤ 0 ≤ 9π.

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Q: 3x + 2y = 6; x = 0; y = 0; axis OY. Find the moment of inertia.

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Q: 2 5 6z³ -8z¹+2z² 4 Z dz

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Q: Solve ₂(x + 1)(x + 2)²(x²-1)dx with and without the even-odd theorems (show both solutions).

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A: Given that; Cost function and revenue function.

Q: Calculate the integral approximation Se for S6 = = ← [²5+ dx.

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Q: Find the length of the curve from the entire hypocycloid 2 2 x3 + Y³ = a³.

A: Explained below

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A: I have shaded the area green which is to be calculated

Q: ds π Find a particular solution of =10csc² 2t determined by s= 2 when t == . — = dt

A: Given:ds/dt=10csc^2(2t) To find: solution at s=2 and t=π/4

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Q: Determine if the function √x² + y² +1 x² + y² f(x, y): 1 2 is continuous at (x, y) = (0,0). If not,…

A: To find whether the given function is continuous or not at(0,0).

Q: FIND THE AREA BOUNDED BY THE PARABOLA x = 8+2y-y², THE Y-AXIS, AND THE LINES y = -) AND y = 3

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Q: (b) The function y(x) satisfies the inhomogeneous second order linear differential equation d²y dy +…

A: We have to find the general solution of the given differential equation using variation of…

Q: 5. x x2 + x − 6 dx

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Q: 3 S₁² √(√²-√²)³ at dt

A: Using substitution method, integration is solved.

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A: We have to apply Stoke's theorem.

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Q: A bucket that has a mass of 25 kg when filled with sand needs to be lifted to the top of a 20 meter…

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Q: An investment of $18,000 was growing at 6.5% compounded semi-annually. a. Calculate the accumulated…

A: In this question we have to find the following given Compound Interest.

Q: Integrate the following functions f(x)=Ln [sec (x)] [², 3]

A: We will see the graph of secx to judge the value of greatest integer function of secx.

Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

A: First we draw the curves, y=6-x2.y=x,y=-2,x=-2.

Q: [* [b3 - 3 3 dy

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Q: Let r(t) = t - sin(t) and y(t) = 1- cos(t) All answers should be decimals rounded to 2 decimal…

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Q: 1. Evaluate the line integral of E = xax - y ay along the segment P₁ to P2 of the circular path as…

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Q: d/dx(arctanh(2x)) 2XIn2 A. 1-4X 2x B.- 1-4X 2 In2 C. 1+2x 2x D.- 1-2x

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Q: dy Find the complete solution of 2e2¹ cosx- dx Note: [e"du=e" + C - sin² x = 0.

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Q: Find the volume generated by revolving the area bounded by y² - 4y - 4x + 4 = 0 and x = 1 about the…

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Q: -0.45|-2.8x - 4.06| 2.5

A: Here we have -0.45-2.8x-4.06-2.5

Q: Find a particular solution of =(x-1)² if y=-21 when x=-3. dy dx

A: Given differential equation is;…

Q: If fx √1- x4 dx = ge ½ A B 0 C D) 1 H|2 H|4 g(e) de, then 9

A: We can solve the given integral by using substitution.

Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. sin (2x - 6) sin(4x12)…

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