Sketch the figures and show step by step solutions. Find the area between the curve y = x3 – 6x2 + 8x and the x-axis.

Q: Evaluate the following integral using change of coordinates: SR S x³ + xy²dady where R is the region…

A: Let's solve given double integral.

Q: Problem 1. Solve these integrals using substitution (a) [ x(x r(x - 2)5dx, (b) [te²³² test dt.

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Q: The vectors u = (5, −4, 0) and v = (5, -4,0) and v = (−4, −5, 4) are orthogonal. Select one: O True…

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Q: J sin²(x) cos(x) dx

A: We have to evaluate ∫sin2x cos2x dx.

Q: Find an algebraic expression equal to sin (cos-¹ (5x-3)). (You may assume that − <cos-¹ (5x − 3) <…

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Q: The z-transform of [n] = u[-n] is

A: Using Z transform

Q: The equation of plane through (3,-1,7) and perpendicular to the vector n(4,2,-5) is 4x + 2y5z-25 =…

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Q: B (2x + 3y² +42³) dV, where B = {(x, y, z)|0 ≤ x ≤ 1,0 ≤ y ≤ 2,0 ≤ #≤ 3} 08 192 170

A: dv = dxdydz And put the limit of integration.

Q: fx tan x x dx

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Q: (g) y dx = (y - xy²) dy Oseparable exact linear in x linear in y Ⓒhomogeneous Bernoulli in x…

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Q: Write an equation of the line below. -8 -7 -6 -5 -4 -3 -8 -7 -6 5. 4 6 17 8 X

A: Solving the problem by finding the value of the problem.

Q: Define R as the region that is bounded by the graph of the function f(x) = -2e, the x-axis, x = 0,…

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Q: Calculate the definite integrals (a) I₁ =¹7 (2x − 1)(x + 2) dx - 18 (b) I₂ =2₂¹8 (x + 2)(√√x - 2) dx

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Q: Matrix has only one row call Row Matrix. multiply a matrix (A) by another matrix (B) if the number…

A: We check the given statements are True or False.

Q: Let à = and b = . Find k so that a and b will be orthogonal (form a 90 degree angle) k-

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Q: Q31 Find the Laplace Transform to the following function L sin2t cos3t

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Q: - If f(x, y) = cos(2x) − x² e5y + 3y², then fxy = -10x e5y True O False O

A: A detailed solution is given below.

Q: 11. Use the comparison test to determine whether 8 k=1 2k 4k + 5 converges.

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Q: 3. Solve below definite integrals (a) [²3test d (b) ["* dt, 3tedt, ["¹ (c) In(x) -d.x,

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Q: Q2\ Choose true or false from the following sentences:- Matrix has only one row call Row Matrix.…

A: 1- true Matrix having 1 row is called row matrix.  2- true.  Gauss Jordan method is used to find…

Q: The geometric representation of the equation is a circle in R3. Select one: O True O False -3x²-3y²…

A: Given: -3x2-3y2=-18

Q: Q5 \ Find a root of an equation Bellow by using Bisection method Where the accurate to at least…

A: Here we have to use the bisection method for the solution.

Q: Differentiate ex with respect to x, assuming that y is implicitly a function of x.

A: Here we have to use the concept of implicit derivative

Q: The orthogonal trajectories of the family of curves r = c(cosec 0 + cot ) are given by: (a) ke-cos e…

A: See this solution in below

Q: Solve the given differential equation by finding, as in Example 4 of Section 2.4, an appropriate…

A: Given: 8-12y+e-3xdx-4dy=0

Q: If √²₁ √√1-y² x² + y² dxdy is changed to equivalent integral in polar coordinates, then the…

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Q: The area enclosed by one petal of the polar curve r = cos20 is False True O

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Q: Find all solutions of the equation in the interval [0, 2π). cos3θcosθ+sin3θsinθ = -1 Write all…

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Q: 2. Use a trig substitution to evaluate S dx x³√²-16' x> 4.

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Q: The graph off-1 is given below. Graph the tangent line to f-1 at the point P(1, 1) for f(x) = -x³ +…

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Q: - If f(x, y) = cos(2x) − x² e5y + 3y², then f xy = -10x e5y True O False O

A: I have stated the used formulas in the solution.

Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz ,at the point P. (0,0,0) in the…

A: We have a given function g=3e^x cos(yz)

Q: The evaluation of 2xe³ dxdy is 3e-1 O e-3 e-1 O None of them O -3e

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Q: The Cartesian equation equivalent of polar equation r = 4tane sece is y True False O

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Q: Verify that y = c₁ex + c₂e4x is a solution to the DE: y" - 5y + 4y = 0.

A: We are authorized to answer one question at a time, so we are answering the first one, please repost…

Q: H.W: find dz and əz | ди ὃν z = 4e* ln y, x = ln(u cos v), y = u sin v as functions of u and vif:

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Q: Match the given differential equation with one or more of the solutions. (Select all that apply.)…

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Q: Find the arc length function for the curve y= 2 x 3/2 with starting point P (1, 2). Select the…

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Q: The length of the curve r = sin² for the period 0 ≤ 0 ≤ π is 2 6 2 O 8 O 4 O None of them O

A: The objective of the question is determine the length of the curve given in polar form.

Q: The integrating factor for the differential equation (xy³)dx + (x²y² + 1)dy = 0 is

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Q: fx x tan x dx

A: We can find the integration using integration by parts as below.

Q: ·S In (x) √xln(x)-x =dx

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Q: The angle between u = 3i- j - 2k and v= i + 2j- 3k is O 60° O 30° 180° 45° 90° O

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Q: Use the graph to determine whether each statement is true or false. lim f(x) = f(3) x → 3 True False…

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Q: Evaluate the following integral using change of coordinates: SR S x³ + xy² dady where R is the…

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Q: The particular solution (yp) of the equation y" - 3y' + 2y = 5 e* is yp = -5xex False True O

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Q: The graph of y = f(x) is shown. Use the graph to answer the question. 2 1 f(x) 1 -1 -2 2 lim Find…

A: Given graph of function y = f(x)

Q: The directional derivative of f(x, y) = xey + cosxy at P,(2,0) in the direction of the vector 3i -…

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Q: Determine whether the integral is convergent or divergent. LA* +4 convergent O divergent dz

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Q: Find the total area of the shaded regions. (-3,36) -6 ₂ Ау 40 32- 24- 16- 8- -8- y=4x (3,36) y=x 5x…

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