H.W: Find the center of mass of a solid of constant density & bounded below by the disk R: x² + y² <4 in the plane z = 0 and above by the paraboloid z=4-x² - y² c.m. 2=4-x²-y² 20 x² + y² = 4

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

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Q: plz provide answer for question asap

A: Please see the below picture for detailed solution.

Q: ₁ y २ The circle x² + y² = 36 ty revolved about the = line 1. Phat is the Volume ? garcratid Cl.…

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Q: Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve…

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Q: Find the derivative of the function y - 4 sec¯' (x + 2). (Use symbolic notation and fractions where…

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Q: Approximate the change in the volume of a sphere when its radius changes from r = 40 ft to r=40.1…

A: We have to given volume of sphere in term of r

Q: 28. Using the method of "First Principles" and showing all steps, determine the -3 2x-1 properly…

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

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Q: Given f''(x) = - 25 sin(5x) and f'(0) = 2 and f(0) = -6. Find f() =

A: In this question, we want to compute the value of f at the given point.

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

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Q: 1 (x-2) +- -(x - 2)²_ -(x-2)³ +...+ 25 1 125 1. Given the series 1- 1 —— (a) For what values of x,…

A: Solve the given series as following:-

Q: fx x tan x dx

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

Q: 10) If 2 an = 12, then lim an = 848 n=1 (A) 1 8 (A) If lim 11) Suppose an > 0. Which of the…

A: Note:Our guidelines we are supposed to answer only one question. Kindly repost other question as the…

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: 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: (A) 3y²ex+y²dx (B) 3) [3y²e²+ y² dx 0

A: In both integration we have to integrate with respect to x . So we treat y as a constant &amp; solve…

Q: The Maclaurin series of the function f(x) = 8x² sin(6x) can be written as f(x) = Σ₂² n=0 where a few…

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Q: Consider the function f : [-1, √10] → R defined by { 10 8 6 T 2 0 -1 f(x) = r², r>2; x≤ 2. I Answer…

A: Disclamier: Since you have posted multiple a question with multiple sub- parts , we will solve first…

Q: Eliminate the parameter t to find a Cartesian equation in the form z = f(y) for: [z(t) = 3t² y(t) =…

A: We can express x in terms in terms of y as below.

Q: Problem 3. Solve below definite integrals In(x) (a) fate" dt. (6) fated. (c)(3) dz. 3te5tdt, 31…

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Q: Part 1 of 3 (a) Graph f(x)=3|x for x S

A: Solution ) f(x) = 3 |x|  x&lt;0 Vertical dilation of scale factor 3 f(x) = -3x and x&lt;0

Q: Q4\Use Cramer's Rule to find the values of x, y, and z from the following equations: 2x + 3y - z = 1…

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Q: FR Find the absolute maximum and absolute minimum of the function f(x) Enter an exact answer. If…

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Q: The vectors u = and v= - are not parallel if and only if Select one: O True O False x = 18

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

Q: 1) / sen(x) 4+ cos²(x) I 1+4x² 2) [√5/2 S² 3) 0 4) 1 x² - 2x + 2 dx √ √2/2 are 0 X dr √2/2 arccos(x)…

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Q: ·S In (x) √xln(x)-x =dx

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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: Use a fixed-point iteration method to determine a solution accurate to within 10-2 forx-3x²-3=0 on…

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Q: If a x i = 0 and a x j = 0, then Select one: O O a is equal to k a is any vector perpendicular to i…

A: We know that if two vector are collinear then their cross product is zero, Therefore 'a x i =0 '…

Q: H.W: replace the following polar equations by equivalent Cartesiana equation, then describe or…

A: Basic conversion ways of polar form to Cartesian form are used along with concept of geometry.

Q: the region of integration, reverse the order of integration, and evaluate the integral. 10 xy 20 Xe…

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Q: find the divergence of F. I Y F(x, y) = -√2²17³1 + √z²+z³³ +y O div F = 2(x+y+z) O div F= 1 1²+y²

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

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Q: Graph the function. y = 3 Plot five points on the graph of the function: one point with x = 0, two…

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Q: Domain star tree door cloud O Function O Not a function Relation 1 O Function O Not a function Range…

A: Solution

Q: The equation of the plane that passes by P(2,0, -1) and that is perpendicular to the line x-5 2-y Z…

A: The plane passes by P2,0,-1 and that is perpendicular to the line x-5-2=2-y4=z-23

Q: The sum of the geometric series Two (n=2 4n+1 n=0 5n-2 is

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Q: 3 Find the Maclaurin series of .Write your answer in sigma notation. 1 + x O O O Σ(x)³n n=0 3…

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Q: The Eigen values of the matrix A = = 1 1 li 1 0 1 1 0 0 1 0,1,2 O 0,0,1 O 0,2,-1 O 0,-1,2 O 0,2,2 O

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Q: 5. f 3√xdx

A: Topic = Integration

Q: a = 6i + 4j + 8k and b = 9i – 6j + 12k. a) [ and b are orthogonal, parallel or neither. b)[ >]…

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Q: X Evaluate the integral [sincos dx. X sin cosdx= 5 C

A: The objective of the question is evaluate the indefinite integral.

Q: Repeat Exercise 60, except with these derivative boundary conditions: y'(0) = 0, y'(π) = 1. In part…

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Q: f(x, y) 4xy; R is the region bounded by the graphs of y = V1 - = x² and y = 0 for 0 ≤ x ≤ 1

A: Solution is given below:

Q: B-Find the area of the region inside the curve r-1+cose and outside the curve -1 and graph the two…

A: Equate both equations to find limits and intersecting points of these curves

Q: 2" The value of p for the series En=1 by using ratio test is n! -1 O 8 2 0 ( 1 O

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Q: dx 16. S sin Ex di √x u= √√x du= I u 12/12 dx = ५५ -1/2 dx 2 би du YN

A: Solve the integration

Q: Using Linear Coefficients of Two Variables, solve: (2x - 5y + 3)dx - (2x + 4y - 6)dy = 0

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Q: Q5: A- Find the mass of the region cut from the sphere x+y+z=a² by the cone z = √x² + y² if the

A: We have to find the mass of the region cut from the sphere by cone.

Q: Q4\Use Cramer's Rule to find the values of x, y, and z from the following equations:

A: We have to find the value of x, y,z from the given system of equation by the camer's rule.