State what the Divergence Theorem says, using your own words. You may assume that E is a solid in R³ and S is the boundary surface of the solid.

Q: Solve the following using the inverse matrix method: (Show your solution) 13 3x + 2y 5 x + 4y 5x + y…

A: As per bartleby guidelines we only give first question answers.

Q: a) b) 1 2 3 + 2.2 3.2² 4.2³ 1 1 1 1 + + 1.3 2.4 3.5 4.6 + + 4 5 5.24 6.25 1 + n(n+2) + + +. 1…

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Q: dr 2√x+3+x d. ·S e. dx x√4x + 1 SIV f. dr x√4x²+1

A: These questions can be solved using integration by substitution.

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Q: 1. For the vectors v = and u = a. Find vou b. Find ||v|| and ||u|| c. Find the angle between v and…

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Q: Let r(t)=(3-2 cost)i + (2+2 sin t)j. Find the arc length parametrization in term of the arc length…

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Q: -4 -3 -2 -1 NWA -1

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Q: 4 Find the general Solution of the following PDES • з Их + 2 Иу -Х u(x,c) =4е 2 (зу-2х)12 ans3- и(x,…

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Q: of 14 that Suppose newly-baked cupcakes are taken out of the oven which is set at 100 degrees. Room…

A: We will use Newton's law of cooling to solve this question.

Q: Which of the following graphs is the correct plot of y = 5+ 5 4 4 -3 3 2 2 -1 + 5 6 2 4 -1 -2 --3-…

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Q: f(x) = 4√x + 2x1/2 – 8x-7/8 + x2 1 23 +2

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Q: 16+19+22+25+...Which one of the following is the sum of the first 90 terms of this series? a)16,701…

A: Concept: Arithmetic Progression: Arithmetic Progression (AP) is a numerical series in which the…

Q: √ √ 1 √x² - 2x + 5 dx

A: Indefinite Integration

Q: 8. Use the given graph to estimate the left Riemann sum for the given interval with the stated…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: dx | | dt dy dt dz dt = 3x + 2y + 4z = 2x + 2z = 4x + 2y + 3z

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Q: 9 of 11 Approximate the area using a. Left Riemann Sum b. Right Riemann Sum c. Midpoint Riemann Sum…

A: Find out  the area using following Riemann sums.

Q: Solve for y at x=2: (x5 + 3y) dx - x dy = 0; x=1, y=2

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Q: Solve the given differential equation. All solutions should be found. (3y² + 2xy) dx - (2xy + x²) dy…

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Q: Q1/ Solve the initial value problem (IVP) of the differential equation by using the appropriate…

A: Concept: Initial value problem: An initial value problem is a difficulty in determining a function y…

Q: a) Sdx 5

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

Q: da d²y +6- dx dx² + 11 dx+6y = ex + cosx бу

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Q: Use integration by parts to evaluate the integral. 9x Saxe dx dx = S4x ex

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Q: Test for convergence/divergence, State the theorems used.

A: As per guidelines, I can answer only one question. Since questions are not interlink with each…

Q: convert the following differential equation into a Perfect equation and then Find its general…

A: To find the solution of the given differential equation.

Q: Consider the basis S - (V₁, V₂} for R², where v₁ - (1, 1) and v₂ - (1, 0), and let T:R² R² be the…

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Q: Draw a direction field for the given differential equation. Based on the direction field, determine…

A: We have to draw the direction field for the given differential equation.

Q: Team Alpha was on their night patrol in Mystical Forest when they suddenly noticed that a flare was…

A: here distance we have to find  a = 9.8 v0 = 5 t = 5sec S=?

Q: Given: Let B (x, y, z) = (xz, yz, 3x² - z²). 1. The task is to identify the work done by B on a…

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Q: Set up the integral in terms of h(x) that evaluates the shaded area under the curve and evaluate…

A: Please refer to the image below

Q: Find the area bounded by y = 2x + x2 - x3, the x - axis, and x = -1 and x =1

A: On solving this we will get

Q: Find the length of the entire perimeter of the region inside r = 18 sin but outside r = 3.

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Q: The cost C of a product is a function of the quantity x of the product: C'(x) = x² - 3000x+50 .Which…

A: Please refer to the image below

Q: 4. A spotlight is on the ground 20 feet away from a wall and a 6-ft tall person is walking towards…

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Q: Convert the Cartesian coordinate (-2,-4) to polar coordinates, 0 ≤ 0 0 Enter exact value. 0 =

A: NOTE: Refresh your page if you can't see any equations. . the given point is

Q: 비신부 4 x² sin(2x) dx

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Q: 5. Set up an iterated triple integral in the order dxdzdy that gives the volume of the solid in the…

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Q: (y² + xy) dx-x² dy = 0, when x = 1, y = 1

A: Solution of given question is written in below steps.

Q: -3t gallons each hour, t hours after a 13. The way Professor Waner drives, he burns gas at the rate…

A: To find out the number of gallons of gas he burns after 13 hours.

Q: √ /1 + x² dx

A: We can solve the integration as below.

Q: S 7. Evaluate 8. Evaluate 9. Evaluate (cos x - sin x) dx cot²x dx (sin x + x) dx

A: Given problems:- Solve the following using the theorems on differentiation. 7. ∫ (cos(x) -sin(x) dx…

Q: Include intercepts and restrictions. Show all calculations.

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Q: 2. Evaluate da da d. Java [. 2 / + 3 + a r/Mr | 1 | dr ar/rº +1

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Q: The radius of a circle is increasing at a rate of 9 centimeters per minute. Find the rate of change…

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Q: Find the absolute maximum and minimum values of the function f(x)-cos²x-3sinx on the interval 0≤x≤7.

A: First I have find the derivative of the given function and set them to zero .Solved them to get the…

Q: Answer it correctly, neatly, and comprehensively.  Written answer only.  A rectangular box with…

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Q: SxVx² √x² - 4 dx

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Q: Find the solution of the given initial value problem. ty' + 4y = t² − t +7, y(1) = 2, t>0 Y

A: We know that a differential equation of the form y'+P(t)·y=Q(t) has Integrating Factor (I.F.) =…

Q: 2. Evaluate Solve all parts or I'll dislike. If you can't solve all parts just skip it da da d. +…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

A: We know that, Newton’s law of cooling is given by, dT/dt = k(Tt – Ts) Where, Tt = temperature of…

Q: Calculate the line integral of the vector-function F(x, y, z) = (y² +2²) i-yzj + xk along the path…

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