Change the Cartesian integral - ² dy dx into an equivalent polar integral. Then evaluate the polar integral.

Q: Identify the open intervals on which the function y=9x-18 cosx, 0<x<2pi is increasing or decreasing.

A: A function y=f(x) is said to be increasing in an interval a,b if for everyx∈ a,b, dydx=f'(x)&gt;0.…

Q: 1. Determine whether the sequence converges or diverges. If it converges, find the limit. tan ¹ n A.…

A: Given;  A. an=tan-1n/n B. bn=Cosn.

Q: 10. The average rate of change of f(x)= x² + x over the interval 0 ≤ x ≤ 4 is a. 20 b. 4 c. 5 d. 1

A: f(x)=x2+xinterval is  0≤x≤4formula for average rate of change is favg=f(b)-f(a)b-a

Q: you have 2 . DU also can you do explain the integration by part showing what you are integrating

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Q: 16. A limit exists if both the right-hand and left-hand limits are equal. 17. A jump discontinuity…

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Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

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Q: For the following function, a) give the coordinates of any critical points and classify each point…

A: The given function is: hx=2x3-24x

Q: An accessories company finds that the cost and revenue, in dollars, of producing x belts is given by…

A: I have appended the formula used in the solution part of the question

Q: Let f(x) = x4 lnx for all x > 0. I

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Q: Find the unique solution to the differential equation that satisfies the stated conditio dy In(x) dx…

A: given:differential equation dydx=lnxxy,  y1=6

Q: Find the derivate of the functions a) F(x) = (7x²-9) (2x + 7) f'(x) = b) f(x) = 8x² - 2 8x +3 f'(x)…

A: To find derivatives

Q: Question 3 Find the value of the derivative (if it exists) of f(x) = (x-2) 4/5 at the indicated…

A: The graph of f(x) is given.

Q: The average rate of change of f(x) = X a. 2 b. 0.5 over the interval 1 ≤ x ≤ 2 is c. -0.5 d. -1

A: we will find the required.

Q: Express the integrand as a sum of partial fractions and then evaluate the integral. 10x² - 1 S 4 X X…

A: Given integral : ∫-10x2x4-1dx To find: The value of given integral using partial fraction. Let I =…

Q: 3. If z=x²y,x=2t+s, and y=1-st², find dz atl=2

A: As per our guidelines, we are supposed to answer only one question at a time. Since you have posted…

Q: Find and simplify the derivative of f(x) = ln(cosh (ax))

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Q: 3. Evaluate the limit for the graph: lim f(x). x+1* y 4 2 01 -2 2 48 x

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Q: Find the tangent plane to the equation z = -4x² + 3y² - 5y at the point (3, 2, -34)

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Q: what about b, thanks

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Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by…

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Q: . In the Gizmo, select sine wave so the parent function is f(x) = sin (x). A. The sine wave is a…

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Q: Find the distance between the point and the plane. (Round your answer to three decimal places.) (4,…

A: To Find : Distance of point (4,6,3) from the plane x-y+2z=10

Q: Find the volume of the region bounded above by the paraboloid z = x² + y² and below by the triangle…

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Q: Let f(x) = -12x sin(x) cos(x). f'(x) at x = ³7. 2 Evaluate ƒ'( ³ ) =

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Q: What is the minimum value of f(x) = x^2 - 8 ln x   on the interval [1,5]

A: To determine the minimum value of fx=x2-8 lnx on the interval 1, 5.

Q: There are two types of license plates. One of them consists of 2 upper case letters followed by 4…

A: We have to slove above question

Q: 3. Select the sine wave so the parent function is f(x) = sin (x). Start with a and b both set to 1.…

A: We have to draw the graph of sine wave with the changing values of b.

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on…

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Q: The integral gives the area of the region in the xy-plane. Sketch the region, label each bounding…

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Q: Find the points on the cone ² = x² + y² that are closest to the point (5,2,0)

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Q: 26. Distinguish between average and instantaneous rate of change, use an answer. appropriate example…

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Q: A 200-foot cable weighing 5 pounds per foot is hanging from a winch 200 feet above ground level.…

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Q: - Find formulas for dy and Ay if y = x² − 7x + 4. **** dy Ay

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: 17x³ (In x)² dx =

A: The given integral is: ∫17x3 ln x2 dx

Q: Find the volume of the solid generated by revolving the shaded region about the x-axis. 6 X₁ = 1, X₂…

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Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

A: To find where the function is increasing or decreasing.

Q: Find the directional derivative of the function f(x, y) = ln (x³ + y³) at the point (2, 3) in the…

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Q: Find the limit. lim 0-0 cos(0) 1 sin (0)

A: Given limit limθ→0cosθ - 1sinθ

Q: 10x3-8x4+2x3 2 2 X→0 15x4+3x3-5x Evaluate Lim

A: We need to find the given limit limx→010x43-8x34+2x2315x24+3x23-5x

Q: A volume is described as follows: 1. the base is the region bounded by y = e³.5x, y = 3.5x² + 0.9…

A: Given,             A volume is described as follows:             1. the base is the region bounded…

Q: Determine if the series O O A n = 1 ² n2 +4 5 n2 + converges or diverges and choose the option that…

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Q: 3) Curve Sketching: The function y = f(x) and its derivatives are given below. Use the information…

A: We have to plot function using given information

Q: 2. Determine whether the series is absolutely convergent, conditionally convergent, or divergent. ∞…

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Q: 1 e) lim (-—-—-₂--²-4) x-3x-2

A: M=limx→3(1x-2-4x2-4)

Q: A study of the demand for air travel between two cities depends on the airfare according to the…

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Q: Find the derivative of the function. f(0) = cos(0²) f'(0) = =

A: Given   f(thita) = Cos(thita2)

Q: (6x² - 4)² 24x dx

A:

Q: Differentiate. h'(0) = h(0) = 0² sin(0)

A: Derivative

Q: 1. Simplify the expression, that is, rewrite the following expressions as algebraic expressions of…

A: (a)  J=sec(arctan(x3))lrt tan-1(x3)=ytan(y)=x3we know 1+tan2x=sec2x