As a trainee spy your mission is to find the volume of the solid region bounded below by the xy-plane above the function z=2x/(x2+2y2) and on the sides by the planes y=x, y=4x, and y=4 by setting up a double integral and evaluating.  b. Draw the region in the xy plane and explain why you should integrate with respect to dxdy. Why is integrating in the order of dydx harder to do here?

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then ...

A: Now

Q: Find the arc length of the following curves on the given interval. 1 for 1 8y2" X = + 4 y . 2

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Q: solve the given differential equation 8. dy /dx = − x /y

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Q: It is known that the temperature of the water boils at 1000C and while it cools, its temperature dro...

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Q: Evaluate

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Q: Verify the following properties for ƒ(x) = sin x and p3(x) = x - x3/6:                    ƒ(0) = p3(...

A: We first find the derivatives

Q: 6.y″ − 2y′ + 6y = 0

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Q: Find the point(s) on the surface z = 3 − x2 − y2 + 6y, at which the tangent plane is horizontal.

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Q: ty?. Evaluate lim 2,3 (1, y, z)(1, 1, –1)

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Q: find the curve’s unit tangent vector. Also, find thelength of the indicated portion of the curve. r(...

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Q: Problem Set question: A particle moves according to the position function s (t) - e7t sin (6t). Encl...

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Q: Solve the equation. dx 2 dt t+ 4x хе

A: Given differential equation is

Q: You have 50 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle t...

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Q: Graph each side of the equation, tan x = sec x(sin x - cos x) + 1, in the same viewing rectangle. If...

A: Given Data The equation is tan x=sec x(sin x-cos x) +1.   Solve the right hand side of equation tan ...

Q: Find the moment of inertia about the z-axis of a thin shell of constant density δ cut from the cone ...

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Q: Calculating limits Determine the following limits. 4x3 - 4x2 lim xS1 x - 1

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Q: Speed and arc length For the following trajectories, find the speed associated with the trajectory, ...

A: Given Data The function is r(t)=<13 sin 2t, 12 cos 5t, 5 cos 2t>. The interval is 0≤t≤π.   Dif...

Q: Solve the equation 2x3 - 3x2 - 11x + 6 = 0 given that -2 is a zero of f(x) = 2x3 - 3x2 - 11x + 6.

A: Given equation, 2x3 - 3x2 - 11x + 6 = 0 One  zero is -2. x = -2 x+2 = 0 So one factor is (x+2). Henc...

Q: The half-life of palladium-100 is 4 days. After 20 days a sample has been reduced to a mass of 0.375...

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Q: Evaluate the indefinite integral

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Q: α=5β=8γ=13λ=2θ=5η=3ω=2

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Q: Let P and Q be points in R2. Show that a linear map G(u, v) = (Au+ Cv, Bu+ Dv) maps the segment join...

A: Let P and Q be two points in R2. We have to show that a linear map G(u, v) = (Au + Cv, Bu + Dv) maps...

Q: state the contrapositive and converse.If today is Tuesday, then we are not in Belgium.

A: contrapositive ="If we are not in Belgium then today is not Tuesday."    

Q: of a moving point The position vector : Ret) = ti +[In cost)];" is given as Find : (a) The speed uni...

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Q: A triangle has sides of length 10cm and 12cm and has an area of 50 sq cm. a) Find the possible appro...

A: Given: The area of the triangle is 50 sq.cm and the two sides of the triangle are 10 cm and 12cm. Fo...

Q: Find a polynomial function of degree 4 with the zeros - 1 (multiplicity 2) and 1 multiplelty , whose...

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Q: Finding r from r' Find the function r that satisfies the given condition. r'(t) = ⟨0, 2, 2t⟩;      r...

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Q: Use the gradient to find the directional derivative of the function w = 5x2 + 2xy − 3y2z at P (1, 0,...

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Q: Sketch a graph of the polar equation  r = −3 cos 2θ

A: We will make a table for the function.  

Q: - 4y² - 5y dx

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Q: 45–46 - Maximum and Minimum Values A quadratic function is given. (a) Use a graphing device to find ...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Graph the vector function r(t) = (cos t)i + (sin t)j + t k.

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Q: What is a perfect square trinomial and how is it factored?

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Q: Use the Product Rule twice to prove that if f, g, and h are differentiable functions of x, then

A: Let us assume f(x)*g(x) together. and h(x) separate.  Then apply the product rule  

Q: Use the graph to determine a. the function’s domain; b. the function’s range; c. the x-intercepts, i...

A: As per policy, only first three parts are answered.

Q: Use a graphing utility to obtain a complete graph for the polynomial function f(x) = x3 - 6x - 9 . T...

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Q: describe the given set with a single equation orwith a pair of equations. The set of points in space...

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Q: Solve the absolute value equation or indicate the equation has no solution :   2 l4 - (5/2). xl + 6 ...

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Q: Use the graph below of f to state the value of each quantity, if it exists.  (If an answer does not ...

A: From part a to c  The Left hand limit is not equal to the Right hand side limit. So for f(2) limit d...

Q: The temperature of the water boils at 100 degrees Celsius and while cooling, the temperature of the ...

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Q: Separate the equation (1 + x + y + xy)y' =x.

A: First, convert the expression on the left-hand side in product form and then separate the equation i...

Q: The annual yield per fruit tree is fairly constant at 150 pounds per tree when the number of trees p...

A: Given: annual yield per fruit tree is fairly constant at 150 pounds per tree number of trees per acr...

Q: Use the Rational Zero Theorem to list all possible rational zeros for the function f(x) = 3x4 - 11x3...

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Q: Solve the unsolved equations according to the derivative below.

A: This is a differential equation of order 1 and degree 2. We usually solve the differential equation ...