The area of the region inside the circle r = 6 cos 0 and outside the cardioid r = 2(1 + cos), a > 0 is

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A: The given function is: z=fx,y=-4x3-6y2-7xy   As we know that; The Power Law: ddxxn=nxn-1

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A: Solution :limx→7fgx=fg7=f2       g7=2

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A: Given  θ=34.2° B=2.27mT F=9.44×10-17 N

Q: Evaluate x³e¹dx O 4 0-etz ext of¥ + + C + C + C 0e**. + C

A: The given integral ∫x3ex4dx

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A: Follow the procedure given below.

Q: Sketch the region R whose area is given by the iterated integral. 8 8-x [*ª [* dy dx + £® ® - * 8 y…

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Q: Find the general solution of the given second-order differential equation. 25y" - 15y' - 4y = 0…

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Q: part, and you will not be able to come back to the skipped part. Tutorial Exercise Solve the…

A: The given differential equation is;  y''+3y'+2y=1/(8+ex).

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Q: Which of the following is a power series representation of f(x) f(x) = Σ(-1)". n=0 8 x2n f(x) = Σ 16…

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Q: Determine whether the given set of functions is linearly independent on the interval (-∞o, ∞o).…

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Q: We have found the following Wronskians. W = −e-³x; W₁ = −e-²x (4 + ex)-¹; W₂ = e¯x(4+ e*)-¹ Р We…

A: NOTE: Refresh your page if you can't see any equations. . here we have

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Q: Use sigma notation to write the sum. 4 4 1 + 2 1 + 3 4 1 + 1 + + + ... + 4 1 + 19

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Q: is 2 Sinh xt sinh (۱) Let y emx (to) be the trial solution to the Corresponding homogeneous equation…

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Q: Find three positive numbers x, y, and z that satisfy the given conditions. The sum is 40 and P =…

A: Given that    Three positive numbers x,y and z                The sum of these numbers is 40.…

Q: Find the average value of the function over the given solid. The average value of a continuous…

A: Average value of the function = 1V ∫∫∫E f(x,y,z) dzdydx .

Q: What is the domain of the reciprocal function of f(x) = 5x+1? {x € R\x2} c. b. (x=Rxs-) a. d. {x =R…

A: We can answer the question as below.

Q: USE NEWTON-RAPHSON'S METHOD IN FINDING ROOTS f(x) = ex²-2 + √√x + 2-3

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A: Given 16y''-40y'+25y=0

Q: Use polar coordinates to set up and evaluate the double integral f(x, y) = x + y, R: x² + y² ≤ 64, x…

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Q: Find the domain and the range of the function. (Enter your answers using Interval notation.) h(x) =…

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Q: Find the radius and interval of convergence of the power series 】 (−1)” (x+3)” √2n n=1

A: This is a problem related to series and sum calculation. Please follow the procedure given below.

Q: Use the summation formulas to rewrite the expression without the summation notation. S(n): = 8i + 7…

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Q: Match the solution curve with one of the differential equations. f Ala Oy"+y=0 y" - 4y' - Sy=0 Oy" +…

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A: We are asked to find the maximize the profit

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Q: Show that the function f(x,y) = 8x²y subject to 3x - y = 9 does not have an absolute minimum or…

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Q: Consider the following second-order differential equation. 2y" + y = 0 Find all the roots of the…

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Q: Find the integral of So 7x+2x² (x-4)(2x+3X2x+1) dx

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Q: Find the general solution of the given second-order differential equation. 3y"+y' = 0 y(x) = =

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

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Q: 1. Find and classify all critical points of the function f(x, y) = x² + y²-3x - 4y.

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Q: Find az/ax if - z = x² sin(xy³) O x³y4 cos (yx³) + 4y³ sin(x³) O x³y³ cos (xy³) + 4x³ sin(xy³) x4y³…

A: Find the derivative

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Q: xy³ lim (x,y) (0,0) x²+2y6, O a. Does Not Exist O b. Infinity О с. 0 O d. 1/3 =?

A: limx, y→0, 0xy3x2+2y6

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: Given: f(x)=1+3x-5x3