Evaluate the given integral by changing to polar coordinates. (a) ff xy dA, Where D is the disk with center the origin and radius r = 3.

Q: Find the total area bounded by the x-axis and the curve y = f(x) on the indicated interval Enter…

A: Use the definite integration to find the area under the given function with x-axis.

Q: let f(x) be a function ƒ : [0, 1] → [0, 1], ƒ(x) = −4x(x − 1). Let g(x): (-∞, ∞) → [0, 1] be a…

A: Use graph of function f(x)

Q: bacteria is An antibiotic-resistant being cultured for a new antibiotic testing. Initially, 100…

A: Please see the below picture for detailed solution.

Q: Use logarithmic differentiation to find the derivative of xsinxe2x+3 cos² x y =

A: Topic:application of derivatives

Q: k X L n X L n Y d X + dy=o 2 (x²-xy + y²) dx-xydy =o

A: Disclaimer:  Since you have asked multiple questions, we will solve the first question for you. If…

Q: 3. The figure on the right side shows the circumscribed (big circle) and inscribed (small circle)…

A: Given Data : In the figure we have given thecircumscribe  ( big circle ) and inscribed ( small…

Q: f(x) Given differentiable functions f(x) = x² e and g(x) = 3 ln x, the function h(x) is defined by h…

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: Question 1: Let f(x) = x³ - 3x² +4. a) Find the intervals of increase and decrease. b) Find the…

A: Let fx=x3-3x2+4a To find the intervals of increase and decrease.b To find the local maximum values…

Q: For the function f(x) = 3 - (x + 1)³, find the interval on which fi increasing. O a. (-∞, 3) O b.…

A: given   f(x)=3-(x+1)3 for increasing  f'(x)>0dxndx=nxn-1

Q: 6. A big red circle shown in the figure is tangent to five small white circle. (a) If the radius of…

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Q: 1) Find the domain: A]f(x)=√x B)g(x) == C₁h(x)=; D) x(x) = log₂ (2x + 1)

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Q: Question 3 Consider the function f of one variable with equation y = f(x) = ln(a - e*) where a is an…

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Q: Find the equation of the sphere centered at (4, 9,-5) with radius 4. Normalize your equations so…

A: Given :Centered : 4, 9, -5Radius= 4

Q: State whether the following is true or false by differentiation. 1 [cos²(x) dx = x + ¹/ sin(2x) + C…

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Q: Find f'(x) if f(x) = O (x²-5x) (3x²+29x-35) (6x+7)* O(x²-5x) (2x-5) 9(6x+7)² O(x²-5x) (-3x²+27x+14)…

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Q: Express the function h(x) f(x) ‡ x and g(x) ‡ x. a) g(x) = = X 1 x - 1 in the form h(x) = = b) f(x)…

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Q: The cost of purifying a gallon of water to a purity of x percent is shown below. 100 100 - X cents…

A: The cost of purifying a gallon of water to purity of x percent is shown below.Cx=100100-x cents for…

Q: Let a . Find al. -

A: Let a→=1, -5, 4. To find a→.

Q: Let u = (2,6, 4) and 7 = (-1, -2, - 7). Compute the following: ū. v = vu - ||||²

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: Find the Riemann sum Ss for the following information. Round your answer to the nearest hundredth…

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Q: - Given = (-6, — 9) and 2 = ( − 3, 1), find ||v – č|| and ||||- ||||. Give EXACT answers. You do NOT…

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Q: 2 2xy dy = y² – 2x³ dx

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Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

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Q: The revenue and cost functions for the sale of a particular product are given below (where x…

A: Please see the below picture for detailed solution.

Q: 3. 4 Determine the volume of the solid obtained by rotating the region bounded by y = √x, y = 3 and…

A: As per Bartleby guidelines we only give first question answers. Please repost for other parts.

Q: Find the equation of the plane that passes through the point (1, 0, 3) and is parallel to the plane…

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Q: ( 1 Suppose we define a function Blue as follows Blue (s) = 5s²+1. Steven is asked to find Blue…

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Q: 7. Sedx €+2

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Q: 2 Let f(x) = 3x² f(a) = f(2h) = f(w + 3) = - 4x + 16. Find the following:

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Q: If vectors u and are parallel, which of the following are TRUE? O and must always be drawn on the…

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Q: (4) If y ==, then y' = x3 ex (A) (B) 3x²-x³ e4x (C) 3x²-x³ 2ex (D) (E) (F) 3x²+x³ e2x 3x²-x³ e2x…

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Q: Find an equation of the plane through (4, -2, -8) that is perpendicular to the line x - 2 = 5t, y +…

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Q: A particle's acceleration is given by the expression a(t) = 2t3 m/s². The particle was measured to…

A: we need to find the velocity and position of the particle.

Q: 6. Solve for the volume of the solid after rotating the region bounded by y = x³ and y= 2x² about…

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Q: 8xe4y x + 4y ive your answer in unit vector notation; that is, in terms 2=

A: Topic :- application of derivatives

Q: For the given position vectors r(t), compute the (tangent) velocity vector r' (t) for the given…

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Q: Find an equation of the plane that passes through the points (-3, 1, 1), (0, 6, 11), and (1,0, -1).…

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Q: Question 5: Choose the correct answer in each of the following: (1) lim x X-0 X (A) 1 (B) -1 (C) DNE…

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Q: Find the unit tangent vector at the indicated point of the vector function T(A/2) = ( r(t) = et…

A: Given vector r( t ) = e6tcost i + e6tsint j + e6t  k

Q: Suppose the total cost C(x) (in dollars) to manufacture a quantity x of weed killer (in hundreds of…

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Q: One whole + six-eighths - 2/4

A: One whole + six-eighths - 2/4

Q: (5) The value(s) of c that satisfy the conclusion of the mean value theorem for f(x)=on [1,3] is (A)…

A: Given :fx=1xa=1b=3

Q: Consider the curve given by x² – 6y² = 5 – 4xy . x+2y dy dx 2(3y-x) Show that

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Q: Vector 7= (6, -2,-2) has initial point (-9, 12, 6). Find the terminal point.

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Q: Consider the curve defined by the equation y — sin y = x − 1 for 0 ≤ y ≤ 2π Find d²y/dx² in terms of…

A: Solution: To find the second derivative of y with respect to x, we need to first find an expression…

Q: 2. Determine an equation of a circle that satisfies the given condition. Express your answers in…

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Q: Given a 2-dimensional function T(x, y) = 3y² + sin(x) answer the following a) find the expression…

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Q: Find the sum of the given infinite geometric series. a₁ = -8, r=-0.17 O-9.64 O-13.88 O -6.3 O-6.84

A: The geometric series has a1=-8, r=-0.17. We have to find the sum of the infinite series.

Q: The angle between vectors u and 7 is obtuse if and only if Ouv> 0 Ou v < 0 Ou v=0

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