3 f(x) 4 X + 3 3 X³ - 2 √x

Q: = 2 2 x²-3

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Q: du Which of the following is the general solution of dx -xu- ? 2+xu²

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Q: 2. Use the Method of Lagrange Multipliers to find the minimum and maximum values of the function…

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Q: 6. Area of a Region between Two Curves. a. Determine the area of the region bounded by f(x) = (x −…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: f(x) = x +2+1 x²

A: we need to write down the values of x on which the function is differentiable.

Q: r(0) = 4 cos³(0)i + 6 sin³(0)j, 0≤ 0 ≤ 2π

A: Given that : r(θ)=4cos3θi+6sin3θj,      0≤θ≤2π

Q: x - 3 im →3 x² – 3x

A: Evaluate the limit of the function x-3x2-3xas x tends to 3 .

Q: Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by…

A:

Q: Evaluate the following integral by interpreting it in 3 1₁ (2 - x) dx =

A: Graph of  | x | graph of - | x | is reflection of | x | about x axis  graph of 2 - | x | is…

Q: 3. The graph of y = f(x) is given. Match each equation with its graph and give reasons for your…

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

Q: Find the distance from (2, -2, 8) to each of the following. (a) the xy-plane (b) the yz-plane (c)…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3.Please resubmit the question and…

Q: 5. Consider the polar curves having the equations r = 3 sin 0 and r = 1 + sin 0. a. Sketch the…

A: Given curves are r= 3 sin(theta),r=1+sin(theta)

Q: Evaluate lim (x,y,z)→(π,0,3) ze -2y cos(2x)

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Q: (4) Find the area between y = 2 sin x, y sin 2x, x = 0, and x T. Sketch the region.

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Q: Find the solution of the given initial value problem. y"" + 4y' = t; y(0) = y'(0) = 0, y"(0) = 1…

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Q: Question 2 The command integral() cannot be used for. Definite Indefinite Particular Any integrals.…

A: Solution ) command integral () cannot used for  Indefinite integrals  Explanation is given  If we…

Q: Which of the following is not a first order linear differential equation? dP dt = y²-y +2Pt = P + 4t…

A: In a differential equation, when the variables and their derivatives are only multiplied by…

Q: Because of the rainy season, the depth in a pond increases 3% each week. Before the rainy season…

A: given that, weekly increment= 3%  initial depth= 10 feet what is the equation that best represents…

Q: Please show your answer to 4 decimal places. Suppose that f(x, y) = e 2²-2y²-2x-y then the maximum…

A: See this solution in below.

Q: show that both orders yie SS 0 55. dy dx

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Q: Use implicit differention to find an equation of the tangent line to the curve at the given point…

A: Derivative is the key for such problems

Q: 2. The path taken by a particle is a horizontal line as it moves according to the law s = ²²¹ +²²³ -…

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Q: Find the volume of the solid of revolution generated by revolving about the line x = − 4, the region…

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Q: 8. Let s(t) = 2t² - t + 1 be the position of a particle from its starting point, in meters, after t…

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Q: (A) True (B) False The differential equation f(x) dx + g(y)dy = 0 is exact.

A: We know that a differential equation of the form  Mx, y dx + Nx, y dy = 0 is exact if and only if…

Q: Analyze the situation. Identify a reasonable domain and range for the situation. The revenue earned…

A: Here we have to analyse the given situation and find the domain and range of it.

Q: Please show all work on this page. 1. A point moves along the curve y = 2x² - 1 in such a way that…

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Q: Using x = tand Show that coś²o do S GEHT dbx = {cos

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Q: √x+2-2 lim x→2 x-2 ||

A: Given, limx→2x+2-2x-2

Q: Is the statement below true or false?   The differential equation f(x)dx + g(y)dy = 0 is exact.

A: The statement is false.A differential equation Mdx+Ndy=0 is exact if and only if ∂M∂y=∂N∂x. see…

Q: Evaluate the indefinite integral: [32 3z¯³ +4z¯² + 4z¯¹ dz = ← + C.

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Q: b) Use the ratio test to determine whether the series k Σk² +1 converges. If the test is…

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Q: [₂ (1-x-4x³. -2 •3 0 0 (1 − x − 4x³ + 2x5³) dx (5 + 3 cos x) dx 3 x² ex dx

A: Given that  some integration and we solve these integrations by using general property of…

Q: 4. Find the polar coordinates (r, 0) for the point whose rectangular coordinate repre- sentation is…

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Q: a. (27x³y6z12) b. 10-4.1 103.5.10⁰.1 . C. 8³√x²4√y -2³√x√√ys

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

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Q: Solve the initial value problem 11 -x dx - y = ¹²e³; y(0) = -1 dx 8 Find the general solution ● (x²…

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Q: A B Which of the following is an integrating factor for ydx-xdy = 0 ? X

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Q: cos² (x) y' = y + tan x

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Q: 2. a) Find the area inside the graph of r = 8 + cos 0 and the right of y -axis. b) Determine the…

A: Area of a region in polar coordinate is Area=∫∫rdrdθAnd length of a curve in polar coordinate is…

Q: 3. Find the general solution to the DE (x+m) dy =(nx - py) dx where m, n, and p are constants.…

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Q: Differentiate the function. 7 x - 7x² +7 X X y' = y =

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Q: An aquarium 6 ft long, 3 ft wide, and 2 ft deep is full of water. (Recall that the weight density of…

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list.) h(x) =…

A: The given function is h(x)=sin2x+cosx   ,  0<x<2π We have to find the critical numbers of the…

Q: Given: (0, 3.0), (2, 20.6), (4, 72.8), (6, 236.5), (8, 714.0), (10, 2209.7) Use the regression…

A: Given

Q: r'(t), r"(t), r'(t) r"(t), and r'(t) r(t) = 2t²i - 5tj + 5t³k X

A: Topic:- application of derivatives in vector algebra

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis…

Q: f(x) = {in(atsine) at find f'(x)

A:

Q: In Exercises the region. 35. 8 6 4+ 2 2 ++ use an iterated integral to find the area of (8,3) 4 6 8

A: As we know the Power rule: ∫xndx=xn+1n+1+C ; where n≠-1   The given bounded region is: Use the…

Q: If y₁ is the particular solution of the differ- ential equation 3.x² -7 which satisfies y(1) = 5,…

A: dydx-2yx=3x2-7