L 1) For f sin sin 2 2πmx 2nnx sin sin L dx , write the solutions for the following two sets m = 4, n = 2, L = 20 %D m = 6, n = 6, L = 20 %3D

Q: ] Make a sketch of a parabola with a vertex of (2, -1) and a focus of (2,1). Be sure to label all e…

A: Please refer to the image below

Q: 3. Find the area bounded on the right by x+y=2, and on the left by y=x' and below by x-axis. 4. The…

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Q: 3. A body is moving in simple harmonic motion with position s(t) = 3 + 2sin4nt. At what time in the…

A: s(t)=3 + 2 sin4πts'(t)=0+2 cos4πt (4π)s'(t)=8π cos4πts'(t)=08π cos4πt=0cos4πt =04πt =π2, 3π2,…

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Q: Sin 5

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Q: 3 5. Sesx )dx e3x.

A: Solving the problem by finding the values of the integration.

Q: 10. For the function f(x) = -2· ex + 6, find the domain, range, and equation of the asymptote.

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Q: Activity 1.3.3. A water balloon is tossed vertically in the air from a window. The balloon's height…

A: graph of s(t) = -16t² + 16t+32.

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A: We have to find the parametric equations.

Q: B a A b Note: Triangle may not be drawn to scale. Suppose c = 15 and A = 25 degrees. Find: a = b = B…

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Q: An equation of a parabola is given. x^2 = 4y Sketch a graph of the parabola and its directrix.

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Q: Definite Integrals, Average Value (Homework) In a certain city the temperature (in °F) t hours…

A: In a certain city the temperature (in °F) t hours after 9 AM was modeled by the…

Q: Find the general solution of the given differential equation: dy = x²y %3D dx

A: Solving

Q: In a memory experiment, Alice is able to memorize words at a rate given by m'(t) = -0.012t +0.4t In…

A: see below the answer

Q: Consider the differential equation x² y" – 3xy' + 3y = 0. (a) Verify that y = cjx + c2x is the…

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Q: 6. Simplify each of the following using the properties of logarithms: (a) In () (b) log2(VE5) 8y3

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Q: (-() Write the linear system in matrix form. Assume X = dx = x - y + z + t – 1 dt dy dt = 2x + y – z…

A: Given

Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x2 - y2, (7, 4, 33)…

A: Given,  z=x2-y2, (7,4,33)

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A: Graph of  the function f(x) and g(x) are given, we have to find the value of h'(1)

Q: Find the area bounded by the graphs of the indicated equations. 12- 10- 8- 61 4-f(X) 2- X= - 3 X = 3…

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Q: Test the series below for convergence using the Ratio Test. n + 5 54n +2 n=1 The limit of the ratio…

A: The given series,      ∑n=1∞n+554n+2

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A: To find the equation of the plane passing through the point (-7,10,-3) and containing the line…

Q: -X-29 8) x* - 4x - 5

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Q: x2+2x-8 ƒ (x) = x+3 Hole: VA: НА:

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Q: 5. Boat Speed A boat on a river travels downstream between two points, 20 mi apart, in 1 h. The…

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Q: 3. The position of a Roomba is given by the function s(r) = r –21² + 120r, where time, 1, is in…

A: In order to solve this question we need to get the velocity and acceleration function.

Q: Evaluate the triple integral g(z, y, 2) dV over solid B. B = {(x, Y, 2) | 4° 0, y > 0, 5 < z < 8}…

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Q: Find the gradient of the function at the given point. f(x, y) = 5x + 3y2 + 5, (1, 5) Vf(1, 5) =

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Q: Fill in the table and then sketch the vector field. z| y F(z, y) = (, %3D 20 0 2 -2 -2 2 -2 -2| -2 2…

A: Here, to fill the table and then plot the vector filed.

Q: (-() Write the linear system in matrix form. Assume X = dx = x - y + z + t – 1 dt dy dt = 2x + y – z…

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Q: Use geometry to compute the value of the following integrals (this is not asking about total area).…

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Q: 3. Evaluate the following integrals: Cose G = 1+ sin ở) v de Vsin

A: LetI=∫cosθ1+sinθsinθdθPut sinθ=udifferentiate on both sidecosθdθ=duI=∫1u1+uduPut u=v2differentiate…

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A: Given problem:- Find the coordinates of the point(s) on the curve y = √(x + 3) that are closest to…

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Q: Find the gradient vector field (F(r, y, z)) of f(x, y, z) = x² sin(3yz) F(z, y, 2) = (

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Q: 6. Evaluate the integral ex e* +e-xdx

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Q: W: i: Show your work. a) [1, j: Find the exact area of the surface obtained by rotating the curve y?…

A: Follow step 2,3 .

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Q: A chemist needs 8 liters of a 25% acid solution. The solution is to be mixed from three solutions…

A: An algebraic word problem is given. We have to solve it. To solve the problem, we will form an…

Q: in find laplace %3D

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Q: (4, 2) (-4, -1) (a) dx (b) (x) dx (c)

A: