2. Find the volume of the solid obtained from rotating the region R about the y-axis, where R is bounded by the three curves, y = 0, y = , and x = y²+3.

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A: Part (a). The Cartesian coordinates of a point is given, (x,y)=(4,−4) ∵r=x2+y2​…

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A: Step 1:Step 2:Here the graph of the functionsStep 3: Here the intersection point Step 4:

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A: Detailed Explanation: Detailed Reasoning for Each Graph: Graph A: Shape: Decreasing.At x=1, the…

Q: explain how to 12.3.1 from 11.3.6

A: Let's start...Step 1: Understand what 12.3.1 saysTheorem 12.3.1 says:A series with nonnegative terms…

Q: Given y = 4x and y = x² +3, describe the region for Type I and Type II. Type I 8. y + 2 -24 -1 1 2…

A: Step 1: Find Points of IntersectionSolve: 4x = x² + 3 Rearrange: x² - 4x + 3 = 0 Factor: (x - 1)(x -…

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A: We compute the determinant of the 4×4 matrix:⎣⎢⎢⎢⎡​7080​6074​8090​4635​⎦⎥⎥⎥⎤​ We use cofactor…

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A: If you have any problem let me know in the comment section thank you.

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A: Step 1:Step 2: Step 3: Step 4:

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A: Part A).  tan(1217π​) =tan(45π​+6π​) Using the sum formula, =1−tan(45π​)tan(6π​)tan(45π​)+tan(6π​)​…

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Q: 2 X Let = dx Complete parts (a) through (c) below. x-1 a. Evaluate I using the substitution u-x-1 X…

A: Let's see complete, step-by-step solution to each part: LetI=∫x−1x2​dx (a) Substitution u=x−11.…

Q: Use substitution to find the indefinite integral. Зи u-8 du Describe the most appropriate…

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A: The Basic Comparison Test (Theorem 12.3.6, Case A) and the Limit Comparison Test (Theorem 12.3.7)…

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A: We can model the height with a cosine function.The general form ish=f(t)=A cos(Bt)+DwhereA =…

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A: Step 1: Step 2:Step 3: Step 4:

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A: Step 1: What is a Power Series?A power series is an infinite sum of the form:∑ (from n = 0 to ∞) of…

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Q: Force with 800 N and 400 N are acting on a machine part at 30° and 60°, respectively with the…

A: Step 1: Resolve Each Force into ComponentsForces acting at angles can be decomposed into horizontal…

Q: Find and classify the critical points of z = (x² – 8x) (y² – 6y). Local maximums: Local minimums:…

A: STEP 1 ​​ STEP 2 ​​ STEP 3 ​​  STEP 4 ​​  STEP 5 ​​  Conclusion​​

Q: 3. Consider the polynomial equation 6-iz+7z² - iz³ +z = 0 for which the roots are 3i, -2i, -i, and…

A: We are given the polynomial: P(z)=6−iz+7z2−iz3+z4=0 and its roots are  z1​=3i,z2​=−2i,z3​=−i, and…

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A: We are given the graph of the derivative f'(x), and required to determine the local minima and…

Q: Explain why these limits hold in 11.4.1

A:

Q: Let E be the region bounded cone z = √√/6 - (x² + y²) and the sphere z = x² + y² + z² . Provide an…

A: Let's find the volume of the region E bounded by the conez=6(x2+y2)​and the spherex2+y2+z2=z Step 1:…

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A: Step 1: Step 2: Step 3: Step 4:

Q: Find the following exercise

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Q: If a (1,4,2) and b = (−1, −5,3), find |a|, a + b, 3a - 2b, a b, a x b and b × a. What is the angle…

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Q: A ball is thrown into the air and its height (in meters) is given by h (t) in seconds. -4.92 +…

A: Approach to solving the question: Detailed explanation:Examples: Key references:

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Q: 6. A particle moves according to a law of motion s(t) = t3-12t2 + 36t, where t is measured in…

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Q: Answer all  Determine the centre, radius, and interval of convergence of each of the power series

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Q: Example 3.2. Solve the following boundary value problem by ADM (Adomian decomposition) method with…

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A: We have given, [10​30​01​] Part (a).  A homogeneous linear system takes the form Ax = 0 , where A…

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A: Please feel free to comment if you have any questions

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Q: Show how to use "Change of Variables Formula for Integrals" to solve "Separable Differential…

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Q: (9) (16 points) Let F(x, y, z) = (x² + y − 4)i + 3xyj + (2x2 +z²)k = - = (x²+y4,3xy, 2x2 + 2²). (a)…

A:

Q: please show all the work

A: Step 1: Step 2:Step 3: Step 4:

Q: Use sigma notation to write the sum. Σ EM i=1 - n 2 4n + n n

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Q: please show all the work

A: We are given a vector:  v=⎣⎢⎡​237​⎦⎥⎤​∈R3 Part (a): Projection of v onto the x-axisThe x-axis is…

Q: 1 R2 X2 2) slots per pole per phase = 3/31 B = 180 - 60 msl Kd Kol, Sin (no) Isin (6) 2 sin(30) Sin…

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Q: 84 256 cubic inches. Find the dimensions of the of material used (the surface area). A farmer wishes…

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Q: Pls help ASAP

A: We evaluate the limit:             limn→∞​(n4n3​+2n+25n+3​)  Step 1: Simplify the first termThe…

Q: 1. A solution to the differential equation y′′ + 4y′ + 13y = 0 isA. y(t) = e^2t cos 3t B. y(t) =…

A: To find a solution to the differential equation y'' + 4y' + 13y = 0, we need to analyze its…

Q: 2. Find a matrix A with the following qualities a. A is 3 x 3. b. The matrix A is not lower…

A: b. The matrix A is not lower triangular and is not upper triangularDefinitions:A lower triangular…

Q: For the power series ∞ (−1)" (2n+1)(x+4)” calculate Z, defined as follows: n=0 (5 - 1)√n if the…

A: Step 1: Ratio Test (To Find Radius of Convergence)   Step 2: Test the EndpointsThis is a divergent…

Q: 1. 2. In Exercises 1, 2, 3, 4, 5, 6, 7, and 8, use the graph of the function f to find lim f(x), lim…

A: Answer :​ Method 1 :  Method 2 :