Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. y = 4x², y = 24x - 8x² 3136π 3 Submit Answer X

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A: We will find the required dot products for the part a, b and c as following.

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A: We know that limit definition for definite integral is  ∫abf(y)dx=limn→∞ ∑i=1nf(yi)Δy Where, for…

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A: We need to solve D.E.

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A: Solved below

Q: Equations of Order One: Separation of Variables Instructions: Obtain the general solution of the…

A: Explanation of the answer is as follows

Q: -8 --0---0--0 = -5 Given U₁ = 10 9 = -4 -8 | compute the cross products as -5

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

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Q: EXERCISE 56 Evaluate each of the following limits. 1. lim x ln x. Ans. *0. 3. lim x csc 2x. 4. 2.…

A: 1) limx-0 xlnx 2) limx-infinity x sin(pi/x) 3) limx-0 x csc(2x). Repost the next questions.

Q: 3) Find a general solution for the following equations. c) y(4) + 8y" + 16 = 0.

A: The objective is to find the general solution.

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A: Recall: Method of Lagrange multipliers

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A: We can solve as follows

Q: 15 en vi - (-2) ₁² = (-3) - (2) ₁ - (-²), ₁² = V3 = = peform the indicated operations

A: Given query is to find the angle between V1 and V2.

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Q: y = y" x Express y" in terms of x and y. (Use symbolic notation and fractions where needed.)…

A: Topic:- calculus

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A: we us Pythagoras theorem in the figure.

Q: 1) Let f(x) = 2x + 1 and h(x) = 2x² + 4x + 1, find a function g(x) such that, Function Composition…

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Q: Consider the following function. f(x) = 2x³ + 3x² - 36x (a) Find the critical numbers of f. (Enter…

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Q: b) Compute the angle in Radians between ₁ and ₂ Round your answer to 3 decimal places.

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Q: IV. Given the functions f(x) = 2x + 5, g(x) = -x² - 6x + 7, and h(x): = the following. Show complete…

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Q: Which functions is the inverse of the function f(x) O g(x) = O g(x) = 2-3x O g(x) O g(x) O g(x) = =…

A: Given query is to find the inverse of the function.

Q: III. Find the equation of the tangent line to at the point (,0). ge* +cos r = sin r+sinh(2 F

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A: Make a right angles triangle. Assume Sin-1(x)=y and equate perpendicular and hypotenuse side of the…

Q: d) e) U₁U4 = Round your answer to 3 decimal places. V1 V3 = Round your answer to 3 decimal places.

A: Given vectors  v1=8−9v2=75v3=4−6v4=90

Q: Suppose f(x,y)=x3y. At the point (1,2), in which direction does f have the maximum rate of change?…

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Q: 3. Find the derivatives: a) f(x) = 3x³-4 2x²+3 b) DO NOT SIMPLIFY y = (x² + 6x + 2)(²+√x + 3) c)…

A: Given; a) f(x)=(3x3-4)/(2x2+3) b) y= (x2+6x+2)(2/x4 + 3sqrt(x5) +3) c) g(x)=-2csc7x+8sin3x+12tan2x…

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Q: For the part of the solution to the DE shown below, y ln x ln y dx + dy = 0 [y ln x lny dx + dy =…

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Q: 2) Use guessing to find particular solutions to the following equations. d) y" - 2y' - 3y = 2e 10…

A: By guessing to find the particular solution of the following equation. y''-2y'-3y=2et-10 sin t

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Q: c+1 for all real numbers E cical points is negative and the ver is not an integer or with am pe no…

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Q: Equations of Order One: Homogeneous Equations Instructions: Obtain the family of solution of the…

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Q: 8. y = cos(x + y) = ysin(x)

A: derivative

Q: graph below is the function f(x) -4 -3 -2 -1 4 3 2 I→2 My -1 -2- -3 -4 NO Of(2) is defined. Olim Lon…

A: Topic:- calculus and function