Use Shell Method only Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = 2x2 - x3 %3D and the x - axis.

Q: Change the Cartesian integral into an equivalent polar integral. 3 0-x SS (P+y?) dy dx = J JO dr de…

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Q: 1 Determine the values of a, b and c if: 2(a,b,4) +(6,8, c) – 3(7,c,-4) = (-24,3,25)

A: We can solve this as follows:

Q: d.x | – 2x² + 1 b.

A: To evaluate: I=∫x5x4-2x2+13dx

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

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Q: 3. y = e-x and the x axis is revolved about the y – axis. (Answer: t C. u. )

A: Let's find.

Q: Solve the equation on the interval 0s0<2r. cot 0+ 3 =0

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Q: 12 dx Jx3 – 3x2

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Q: 7. Simplify and evaluate. (2x³y²)³ a) (x’y (9y)? b) for y=-2 (3y*)

A: Given: a)2x-3y23x3y-42b)9y23y-13

Q: Зх—5 dx (х+1) (х+2)2

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Q: Evaluate the following integrals i. L Ix| e(1+x*) dx -0.5 ii. So x cosh(x² + 1) dx

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Q: Use Lagrange multipliers to find the given extremum. Assume that x and y are positive. Minimize f(x,…

A: We have to minimize the given function.

Q: x² – 2x – 1 dx I ( – 1)²(x² + 1)

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Q: 3 - 6t +1 x =ť° +• ;teRat t= 4 y=t° - 3t² – 9t –1

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Q: II. Find the Inverse Laplace of the following 2s-9 d. s2 +2 1 е. (s²+1)(s²+4s+8)

A: We have to find the inverse laplace transform.

Q: Given x = 2 lnt and y = 1+t, find the equation of the tangent line when t = 2. %3D O y=-4x-8ln(2)-5…

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Q: 3. Find where the curves intersect, draw a sketch of the region, and compute the volume when the…

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Q: would appreciate the help. 2 questions in 1 photo.

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Q: If the series E, (an)? diverges then lim,00 an + 0 Select one: True False

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Q: What is the absolute minimum value of the function f(x) = x' - 3x² on the interval [-2, 4] ? a. -4 O…

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Q: Jk, when = & Case y: 2 Sing

A: Solution 1:

Q: A manufacturer has an order for 1000 units of fine paper that can be produced at two locations. Let…

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Q: 1. Find the absolute extrema, if any, of the following functions on the given interval. (a) f(x) = 4…

A: Given:     a) fx=4-3x ; (-1,2]           dydx=ddx4-3x                   f'x=-3   There in no…

Q: Use differentials to estimate the relative error in the lateral surface area of a right circular…

A: Relative error

Q: (b) ( )Find the inverse Laplace transform 2 2s +3 (s - 5)(s +3) 82 +4

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Q: -2 is a critical number of the function f(x) = /2x - x2, Select one: O True O False

A: The given function is  f(x)=sqrt(2x-x2)

Q: The size of an unborn fetus of a certain species depends on its age. Data for Head circumference (H)…

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Q: 2x e dx 4е2х —8е" +5 -

A: The integration of the integral is  e2x/(4e2x-8ex+5).

Q: Problem #7: (a) Solve the initial value problem (x - 1)y' - y = 16(x - 1), (2) = 0 (b) Write the…

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Q: The function x2 f(x) 1 - x is decreasing on (0, 1). Select one: O True O False

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Q: Evaluate the following integrals. (csc 0)(1+ sin? 0 + sin 0 cot? 0) de a.

A: This question is based on indefinite integral.

Q: 00 Σ 3k k-2

A: Integral Test : Suppose that f(x) is a continuous , positive and decreasing function on [k,∞) and…

Q: The polar coordinates of a point are given. Plot the point. (2. ) z/2 R/2 2 1 -1 2 1 R/2 2/2 -1 Find…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = - 3 ex cos (yz),…

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Q: The power series representation of 8. f (x) = x+7 centered at x=2 is: O :- 8 8 8 8 81 (*- 2) + (x-2)…

A: Topic = Series

Q: What are the two values of k closest to 1 - 4 for which S sin? (x +4) – cos² (x + 4) dæ has a value…

A: The solution is given in the next step.

Q: (b) Find the values of a and b so that the function f(x) = x² + ax + b has a local maximum at the…

A: Given

Q: Are the Following Vectors Linearly Dependent or Independent? 3) (0,1,0), (2,1,0), (3,4,7) Ans.…

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Q: 3. Let C be the line segment starting at (0,0) and ending at (1.3) (see diagram). Find a…

A: The line passing through (0,0) and (1,3) is given by: y=3x which in parametric form is given by:…

Q: Find (x, y, z). (Let P = (7, 7, 0) and the Midpoint = (0, 5, 5).) (х, у, 2) %3 Midpoint (х, у, 2) P

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Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. You must show your work.…

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Q: Select the correct answer. What is the value obtained by using left endpoints with n= 4 subintervals…

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Q: Use Lagrange Multipliers to solve the following: Maximize f(x, Y, z) = 4.x + 2y + z subject to æ? +…

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Q: 9. Jer'y ds, C:x cos t, y sin 1, z = 1, 0<1s/2 %3D 77

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Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

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Q: 1 y = 6 2.x +

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Q: n3 + n? ) Σ 00 (n – 1)! n=1 2n + 3 n2 In n n=1

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Q: Find the Taylor series generated by f at x=a. f(x) = 1/x2, a= 10

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Q: a. (csc 0)(1+ sin² 0 + sin 0 cot? 0) d0 5.

A: We will solve the integration

Q: Assuming that out of 200 documents, 40 documents are relevant. A search engine returns 30 documents,…

A: We have to calculate the recall percentage.