Suppose that f(x, y) = 6, and D = {(x, y) | x² + y² ≤ 4}. I Then the double integral of f(x, y) over D is f(x, y)dzdy - D

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: The given curves are; x+y=5, y=0, x=0   So, the bounded region is as shown below.   Apply the disk…

Q: The function f(x) = 2x³ − 42x² + 270x – 4 has two critical numbers. The smaller one is x = and the…

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Q: Find a line that is parallel to the line that passes through both P and Q and contains R.

A: We have to find the equation of line.   According to our guidelines we can solve only one question…

Q: Evaluate the double integral: L y 1/3 27 +1 dx dy.

A: Given: I=∫08∫y132yx7+1dxdy The region bounded by the curves x=y13, x=2, y=0 & y=8 is as shown…

Q: Vectors: given vectors "=(-3,-1,4) and v = (-2,3,2) 2u- v Add/subtract/scalar multiplication: Find…

A: Given: u=-3,-1,4    and  v=-2,3,2

Q: solve by differential √226

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

A: Given problem:- convert the following differential equation into a Perfect equation and then Find…

Q: JJ xy²z dv where D is the tetrahedron in the first octant bounded by the coordinate planes and the…

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Q: Solve simultaneously x (t) + x' (t) − y (t) + z' (t) = 4 y' (t) + z(t) = 0 2x(t)+y(t)+z(t)=0 where x…

A: Given the system of differential equations x(t)+x'(t)-y(t)+z'(t) = 4  ......(1) y'(t)+z(t) = 0…

Q: x² - 5y²-3x -y +22=0 (y-2)(x-y-2) = 0

A: Given

Q: QUESTION 2 Given: 2y (y2-x) dy = dx ; x(0)=1 Find x when y=2. Use 2 decimal places.

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Q: A rocket is fired vertically upward from the ground. The distances in feet that the rocket travels…

A: Given :s(t)=-17t2+469t

Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 6…

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Q: 2. The task is to determine the flux of B across G, where G is the positively-oriented portion of…

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Q: conver the Following differential equation into a Perfect equation and then find 1+5 general…

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Q: 4) A manufacturer has determined that the total cost C of operating a factory is C = 0.5x^2 + 15x +…

A: Given, total cost C of operating a factory is C = 0.5x^2 + 15x + 5000  where x is the number of…

Q: Find the area under/bounded by the given curve. Show the graph (you can use any graphing software,…

A: To find the area under the given curve.

Q: Find the slope of the tangent line to the polar curve r = 1 + cos(0) at the point specified by 0 =…

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Q: Solve and illustrate the problem. 1. Find the volume of the wedge cut from a right circular cylinder…

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Q: Use Cartesian coordinates to evaluate JJ v² av where D is the tetrahedron in the first octant…

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Q: Find the solution of the given initial value problem in explicit form. 77 ㅠ sin(2x) dx + cos(8y) dy…

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Q: y4 + y² − 1 y³ + y - dy

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Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

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Q: Solve the given initial value problem. + xy = 2 ²y² + y² = 3 O xy² + xy³ = 0 xy² − y³ = 1 O x²y² -…

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Q: Find the slope of the tangent line to the curve below at the point (5, 3). √x + 4y + /5xy…

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Q: O C. Z= (sin O D. Z= (cos + i cos Write the complex number 9-9√3 i in exponential form. z= (Simplify…

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Q: Find the values of x for which the given function has a maximum or a minimum value using the First…

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Q: Find all values of x in the domain F such that F’(x) does not exist. B.Find the critical numbers of…

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Q: Consider the function f(x) = x¹ − 50x² +11, x¹50x² This function has an absolute minimum value equal…

A: We need to find absolute max. and min. value.

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: Find equations for the tangent line and normal line to the circle at each given point. (The normal…

A: The circle equation x2+y2=25

Q: hand written plz 1 5. Let D be the region bounded by the lines y = x, x=3 and the curve y = r (a)…

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Q: Consider the function f(x) = 3x² − 2x +9, 0≤ x ≤ 7. The absolute maximum of f(x) (on the given…

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Q: If s(t) = 4t³ - 6t² - 24t + 5, where t> 0 represent the position of a particle traveling along a…

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (8x…

A: Given

Q: V1 - (In x)² x ln x VI dx

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Q: Q.1// (A) Use trigonometric substitution to find f- x²-2x-5 x3-5x² (B) Use partial fraction to find…

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

A: A detailed solution is given below.

Q: Find a differential equation that corresponds to the given direction field. Consider differential…

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Q: Given the function y = f(x) defined at all real values of x. Let x = 2, 3, 5 and 7 are critical…

A: According to given, The function f(x) is increasing in (-inf,2) and (5,7) This is because f'(x) is…

Q: B = {x ER: x is a counting number} = {1,2,3,...} C = {x ER: x = 2n + 1 where n is a nonnegative…

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Q: Consider the function ƒ(x) = 2x³ + 9x² − 60x+8, − 5 ≤ x ≤ 3. This function has an absolute minimum…

A: This question is based on application of derivative.

Q: Let f(x) = 3 cos 2x + sin²x. a) b) Show that f'(x) = -5 sin 2x. In the interval <x<3 Find the value…

A: Please see the below picture for detailed solution.

Q: Q1: Find the area of the region that lies in the first quadrant under the curve √x + √y = 1. (Draw…

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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: Problem 4. (. Let C be the curve given by parametric equations r(t) = 1², y(t) = 2t, z(t) = ln t, t€…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

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

A: Rewrite the differential equation in standard form and solve it

Q: Apply Green's Theorem to evaluate the integral. $(3y + x)dx + (y + 5x)dy C: The circle (x - 3)² +…

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Q: f cos 4x dx 2x dx S (x-2)²(x+2) x2 dx √4-x²

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Q: Find the derivative of F(x) = f (t³ - t) ³ dt. O 5 (t³-t) (3t²-1) ○ (x³ - x) 5 ○ 5 (2³-x) 4 O 3t² -…

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