Evaluate the integral by making an appropriate change of variables. JJ₂² 7 cos(3 (y + x)) dA where R is the trapezoidal region with vertices (6, 0), (10, 0), (0, 10), and (0, 6)

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Q: M8 ηχη n=1 3"

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A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Convert the Cartesian coordinate (1,-2) to polar coordinates, 0 ≤ 0 0 r = Enter exact value. 0 =

A: Cartesian coordinate (1,-2)

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Q: Find the radius of convergence and the interval of convergence of the series. n=1 8n-1

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Q: 4. Find the derivative of the following functions: a. y = x² sin x b. y = ex cos x 3 c. y = (x² + 1)…

A: *Note – As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly…

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Q: 5. Example: The graphs of f and g are given. Use them to evaluate each limit, if it exists. If the…

A: A graph of the functions  and  are given.The aim is to find the following,(a) (b) (c) Note:  Since…

Q: d. h(x) = x3 3 -2 - 2x² + 4x, 0≤ x < ∞0 e. f(x) = √25-x², -5 ≤x≤ 5 f. g(x) = 0≤x≤ 1 x-2 x²-1'

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A: I have appended the formula used in the solution procedure

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Q: Refer to the graph shown below and evaluate Ĵ 1941 CH - 4 f(t)dt.

A: Consider the figure

Q: 12T 4. Evaluate in Cylindrical Coordinates D bounded by z= x² + y² and the plane z = 4 ff zdxdydz

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Q: is it 3and -2 for A?

A: y=x2-6x+7

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A: Given,

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Q: 4. 14: I can evaluate a definite integral using geometry or the FTo C. The graph of f is [4, 8] the…

A: graph

Q: If you know that Q(x) is a quadratic function and that Q(5) = 10, Q(8) = 11 and Q(1) = 9 then: 1…

A: If you know that  is a quadratic function and that , then to evaluate the following integral.

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Q: Evaluate ∫∫∫E 1/(x^2+y^2+z^2 )dV where E lines between the spheres x^2+y^2+z^2=4 and x^2+y^2+z^2=16…

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Q: 4. Using Geogebra, draw the parametric curve, x = sin³t+cos³t; y = sin² t - cos²t,0 ≤t≤ 2n-

A: The given curve is,The given interval is,

Q: Starting with an initial value of P(0) = 50, the population of a prairie dog community grows at a…

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Q: 1 e e 5. If A-), then ¹-(3) = eª = 01 0 e

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Q: xp£p( c£xZ+& ,x)_JJ A

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Q: At time t, the position of a body moving along the s-axis is s=13-1512+72t m. Find the body's…

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Q: Solve the following problem and show your complete solutions. 3. Find the area bounded by y = x³; y…

A: To calculate the area bounded by the curvesy=x^3 and y=4x^2

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Q: The amount, A, of 159 grams of a certain radioactive material remaining after years can be found by…

A: Given that the amount A of 159 grams of a certain radioactive material remaining after t years is

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Q: 2) Find S -18 dx

A: The given integral is e1/x.

Q: Find the general indefinite integral. (Use C for the constant of integration.) [(cos x + x)dx…

A: The given integral .The aim is to find the solution to the integral and sketch its graph.

Q: 1-√x)³ 3 √x dx

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Q: 5. Find two antiderivatives of f(x) = x0.8 - 3e²¹ + π cos(2x)

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Q: 19. If $100,000 is invested at 6% compounded monthly for 7 years, the compounded amount is given by…

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Q: 37. se sec² (10x + 7) dx

A: Since you have asked multiple questions in a single request so we will be answering only first…

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A: The position of a particle moving along a coordinate line is s=52+4t, with s in meters and t in…

Q: Express your answer as a polynomial in standard form. f(x)= x - 1 2 g(x) = 3x² - 4x – 12 Find:…

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Q: 3 x¹ +1 dx

A: The given integral is (x4+1)/x2, limit from 1 to 3.