(a) Show that r = 2sinθ + 2cosθ is a circle. (b) Find the area of the circle using a geometric formula and then by integration.

Q: Asap

A: Let's evaluate limits.

Q: Let A = {2,7,8}, B = {-1,2,6,7}, C = {2,4,6,8,10}, D = {{7},{2,4},{6},2 ,8} List each set starting…

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Q: Consider the integral (a) Find the Riemann sum for this integral using right endpoints and n = 3.…

A: Here we have to use riemann sum.

Q: The distance from the point (1, -1, 1) to the point (-3, -3, -3) is 3 AO 5 BO 4 CO 6 DO

A: Solution: Given coordinates are

Q: slve the following I.V.P do +=y=y² Y= da B.C = (P.G.) 56). 1 3

A: Given differential equation:- dydx+12y=y3

Q: Use the method of undetermined coefficients to solve the given equation. dy dx y +2→=5;2 X

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Q: Evaluate the indefinite integral: [ (6e" + 5 sec² u) du = = ← + C.

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Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

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Q: Use cylindrical coordinates. Evaluate III. (x + y + z) dv, where E is the solid in the first octant…

A: Let's evaluate triple integral by using cylindrical coordinates.

Q: Your Mark: Problem #3: Use cylindrical coordinates to find the volume of the solid bounde Enter your…

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: Calculate the third derivative of the function: f(x) = 11 (x + 2)³

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Q: The gravitational force exerted by the planet Earth on a unit mass at a distance r from the center…

A: Let's find given function is continuous or not.

Q: Y=4csc x A, B, C, or D

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Q: the method of cylindrical shells to find the volume V generated by rotating the region bounded by…

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Q: Find the derivative of the function. 6x fox u g(x) = u² - 1 3x u² + 1 du 6x 0 6x • LC² (u) du = [,…

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Q: Find each limit, if it exists. (If an answer does not exist, enter DNE.) x7 +9 (a) lim X→∞ +8 - 8 x7…

A: Limits

Q: Evaluate IdA dA, where R is the region in the first quadrant bounded by y2-x3 and the line y=x. R O…

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Q: Evaluate the following indefinite integral f11 sin(x) - 2 cos(x) dx = +C

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Q: Problem #7: Evaluate the following integral SS 8x + y (5x-y) ln(5x-y) R Problem #7: dA where R is…

A: Here, R is the region bounded by the graphs y=5x-e2, y=5x-e6, y=-8x+9, y=-8x+6. Now, using the…

Q: Solve the following differential equations. xy dx + (x2 - 3y) dy =0

A: Given, xy dx + (x2 - 3y) dy =0

Q: A function and its graph are given. Use the graph to find each of the following, if they exist. Then…

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Q: Find a solution to the separable differential equation that satisfies the initial condition y(1) =…

A: Given query is to find the solution of the differential equation.

Q: The equation of the plane passing through the points (1,3, 2), (3, 1, 2) and (1, 1, 1) is: x-y-z=-4…

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Q: Find the derivative of y with respect to t: y = sec¯¹ (9t5 + 8). dy dt

A: Given; y=sec-1(9t5+8).

Q: You have been given the following differential, equations? which of them linear? na are 2 d²y dx²…

A: The objective is to find the correct option.

Q: 6 Given f(x, y) = 7x* cos(y¹), find fxy(x, y) =

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Q: g(x) = I² +9 sir<1 √x+9x si x ≥1

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Q: 13. 14. Find the indicated limit. lim, (x²+5)(x²-49) Need Help? Find the indicated limit. x¹ +5…

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Q: J. 11 lim X-18 e²x +4 2x et

A: Given query is to find the Indicated limit.

Q: The population of weights for men attending a local health club is normally distributed with a mean…

A: We need to fill in the blanks.

Q: Find for the function y = 17. dy dx

A: See this solution in below.

Q: dy dx y = 9 In x + 3 log gX Find

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Q: Consider the following. y = x³ 3x + 6 -4 -3 -2 relative maxima relative minima horizontal points of…

A: We need to find extrema.

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: 1. 2. 3. 4. 5. Differential Equation d5y dx5 y dx + (2xy + ln y )dy = 0 d³y +4x². + cos2x dx3 d³y…

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Q: (1 - 1) da I +52 +6

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Q: Consider the surface defined by z = f(x, y), where: x²y 2(x² + y²) f(x, y) = Write down the equation…

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Q: Use partial fractions to evaluate the integral. 2x²-1 (4x-1)(x² +1) dx

A: see below the answer and calculation

Q: Find the value of a that makes the following function differentiable for all values of x. g(x) = ax…

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Q: Given f(x, y) = 6x³ — 5xy² + 5y5, find fx(x, y) = fy(x, y) =

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Q: Consider the following. y = 4x³ - 24x² + 9 (a) Find the critical values of the function. (Enter your…

A: Please see the below picture for detailed solution.

Q: I just need help with Question D, please! Thank you!

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Q: Use spherical coordinates. Evaluate III. xyz dv, where E lies between the spheres p = 4 and p = 6…

A: We know x=ρsinϕcosθ , y=ρsinϕsinθ,z=ρcosϕ

Q: Mrs. Smith switches back and forth between her normal self, Alice, and her intimidate alternate…

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Q: dy If −5x² + y² = 5 then find at the point (2,-5) in simplest form. dx²

A: Given the equation: -5x^2+y^2=5

Q: For what sort of problems are the integration techniques of substitution and integration by parts…

A: Integration by substitution mathod is used when two functions are given in the integrand and one is…

Q: dy Find for the indicated function y. dx y = 15* + e 6 dy dx = □ (Type an exact answer.)

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Q: 2. Evaluate the given differential equation and determine the general solution (xy² + y² + 1).dx +…

A: The given differential equation is; (xy2+y2+1)dx + (x2y+2xy+y)dy=0

Q: Use a calculator and evaluate A to the nearest cent. A = $11,000 e 0.03t for t = 4, 8, and 9 If t=4,…

A: Given query is to find the the value of A at different points.