1- Use the shell method to find the volume of the solids generated by revolving the shaded region about the indicated. E D 2 O

Q: Find the derivative of the function at Po in the direction of A. f(x,y) = - 4xy-y², Po(-3,4), A=i+2j…

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Q: A lamina occupies the part of the disk æ² + y² ≤ 1 in the first quadrant and the density at each…

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Q: Sº₁ 1 2 x³ dx x²+x+1

A: Solution of given question is written in below steps.

Q: 3. F(s) : = s² s4 +16

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Q: f (x+2) In (x+2) - 4 tc (x+2) Xt *+ 2

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Q: Suppose F(x, y) = xyi + (x −y)j and C is the triangle from (4,0) to (-4,0) to (0, 4) to (4,0). (a)…

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Q: A man is standing on a horizontal ground 30 ft away from a hot air balloon. After a moment, the hot…

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Q: 1. Evaluate the given integral Q. J[(y - 2x) dA, R where is the region bounded by x = 0, y = x, x =…

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Q: Find the area under a curve whose equation is y = x³-3x²-x+3 From x = 0 to x = 2

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Q: 1 x² dx So √4-x²

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Q: (20-0) Given that = 5and 이히 = 3 1 6. Round your answer to one decimal place. = 3 and that (2a ›(à +…

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Q: dy dx X2 (1+y2)

A: Let's solve given diffrential equation.

Q: 4. Given that f'(x) = −6x² + x + 12 and f(1) = 7, find f(x).

A: Given : f'(x)=-6x2+x+12f(1)=7   To Find : f(x)

Q: A company has a security system that uses digits from 1 to 6. a) How many 3-digit security codes are…

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Q: Mo Tu We Th Fr Sa Su Date Evaluate the following integrals: (show solution) 1 as √ x²+2 b.) f x+1…

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Q: Solve the boundary value problem y" + 4y' + 13y = 0 y(0) = 0 y'(pi/2) = 0

A: To solve the given differential equation

Q: 9) Find the equation of the tangent to the curve y = 1+ Int and x=t+Int when t = 2.

A: Given problem:- Find the equation of the tangent to the curve y = 1 + lnt and x=t+Int when t = 2 .

Q: Find the general equation of the circle of curvature of the parametric equation t+1 X: ; y = ±…

A: This is a problem of finding equation of the circle of curvature. Based on the general formula and…

Q: дz дz Suppose z is a function of r and y and tan(√x + y) = e²². Determine and 3x ду

A: given function tanx+y=ez2

Q: Find the integral of ³y²-y+1 f dy y³-y²

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Q: Assuming 8x³ - 10y² - 2xy = 0 defines y as a differentiable function of x, use the theorem dx dy dx…

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Q: 2 2 dx 2x (V2x + 9)

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Q: Question B2 Consider the vectors, 3 p= and q= 2 (i) Compute 3p - 5q. (ii) Find the length of p, that…

A: A detailed solution is given below

Q: 3) Which two vectors are perpendicular? a = [-10, -2, -4] 6= [3,-3, 6] = [5, 1, -2]

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Q: 1. Evaluate the given integral Q. Q a = 1₁² 1₁² ² (x - y) dx dy 2. Sketch the region of integration…

A: double integral and changing the limit

Q: Find the area of the region bounded by the curve y=x^2-3x the x-axis and the lines x = 1 and x = 2.

A: This question is based on application of integration.

Q: Choose one(1) from the following question to be answer. The graph of each rule must reflect on your…

A: The Trapezoidal Rule: The Trapezoidal Rule divides the whole area into smaller trapezoids rather…

Q: Solve the following problems showing detailed solutions.Draw the complete figures for each question.…

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Q: f cot x dx Select one: a. In sina+c + c + c + c O b. In sec x oc. In csc r od. In cos x

A: cotx = cosx/sinx

Q: Find the area bounded by the line y = x+2 and parabola y = x².

A: We can solve this as follows:

Q: A forest has a population of cougars and a population of chipmunks. Let a represent the number of…

A: Two diffrential equation given with respect to time t. Let's solve .

Q: Evaluate each limit if exist lim x -> 0 (\sqrt(x+7)- \sqrt(7-x))/(2x) lim x ->3…

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Q: Solve the initial value problem 2y" + y' - 10y = 0 y(0) = 0 y'(0) = 1

A: We have to solve the initial value problem.

Q: Siven a = (1, 2, 1) and b - (k. 1, 2) and a × b = √35. X Determine the value(s) of k.

A: Follow the procedure given below.

Q: 6. Evaluate the expression sin cos (77)) 11 tan sin (sin-¹ (²-3)) 13,

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Q: 7. y=4x²-5x is known to be the relationship in a curved archway. Determine the area under this…

A: Note that, the curve y=4x2-5x and x=5 and x=1 intersect at (5,75) & (1,-1) respectively.

Q: Solve the system of differential equations. = - X1 6x1 + 2x2 X2' - 2x1 - 10x2 2, x₂(0) - 22 = x1 (0)…

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Q: If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the…

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Q: 1. Graph the function below Using Calculus, find the intervals where the function increases and…

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Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

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Q: PROBLEM 3: 00 Consider the set S= = {A€M₂×3 ×3 (R): A = -[880] where a > 0, b>0, with the usual -0,…

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Q: x²y" - 3xy' - 2y = 0

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Q: Find binomial coefficient (3)

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Q: Jack has 13 cards printed with the letters from the word “UNDERSTANDING,” so that “U” is in one…

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Q: Evaluate f Select one: cosha -da cosh²a-1 a. -sinhr+C O b. -cscha+C C. O d. -coshr + C none of the…

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Q: du du dx' dy 1) u = 3x²y + xlny² - Inxy 2) u =xe*Y+ ‡ ArcTan , 3) u = +2²-3² I. Find and (whenever…

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Q: lim X→+∞ 5 In³ x 2 X²

A: Let's evaluate limit.

Q: Convert each pair of polar coordinates to rectangular coordinates 1. (2,315 degrees) 2. (1,…

A: 1) We know that relation between cartesian co-ordinate and polar co-ordinates, x=rcos(θ),…

Q: A bolt is being loosened by a 40 cm wrench. The torque in this situation has a magnitude of 12 J and…

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