Consider the following. y 4 3 Find its foci. 2 1 -1 -2 Find an equation of the ellipse. smaller x-value larger x-value 1 (x, y) = 2 3 (x, y) = 4 5 6 X

Q: Consider the function. X 10/17 - 12/24 5 Find Duf(7, 1), where u = cos(0)i + sin(0)j. f(x, y) = 8

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Q: 6. Evaluate the following real integrals by residue theorem 3 • I- 88 151 +47 O dx (x²+1)(x² +9) ans…

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Q: Evaluate the triple iterated integral. LLL Jo π/4 6 6-r rz dz dr de

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

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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: Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not…

A: Topic = Application of Derivative

Q: Find three positive numbers whose sum is 114 and whose product is a maximum.

A: follow the procedure given below.

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: Topic = Differential equation

Q: 4. (x-1)(2x³+2x²+3x+2) dx x³ (x+1) r 5. csc ³0 de

A: We have to integrate question no 4 and 5.

Q: Perform Vector Operations in Terms of Components Write the vector shown below as a combination of…

A: Given problem:-

Q: Evaluate the double integralfor, f(r, e) dA. Sketch the region R. O π/6 8 O sin(0) cos(8) dr de -5…

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Q: Use the geometric series formula x5 1 + x = ∞ n=0 1 1 - Y = ∞ Σy" to express the function as a…

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Q: 7. Determine the intersection, if any, of the planes with equations x +y-z+12=0 and 2x + 4y - 3z…

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Q: Determine whether the vector field is conservative. F(x, y) = (7y - x²)i + (7x + y)j conservative…

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Q: Which of the following planes is normal to the line given as: x = 2t + 3, y = 5t - 7, z = t - 4 O a.…

A: This question is based on dot product.

Q: EX: Show that d² = 2πi where c is a unit § Z circle. C:1Z1 =1 Sol: ie Z= re io dzir e do 24 io ixe…

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Q: Find the (a) derivative y'= dy dx y = (n² + 5 secx) ㅠ of following Question tog 3 x

A: Note: Due to guidelines i can solve only your first question. Solution: a) y=πe+5sec xlog3x…

Q: Evaluate the iterated integral. 2 . (x+y+z) dx dz dy

A: The given integral is: I=∫02∫08∫01x+y+zdxdzdy   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: elax upx dx

A: ∫1xlnx23dx

Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers…

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Q: (4x²y² - x² + 4xy² - x) dx + (2xy + x + 2y + 1)dy = 0

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Q: 7. Determine the intersection, if any, of the planes with equations x +y-z + 12 =0 and 2x + 4y - 3z…

A: Since you have posted multiple questions. As per guidelines we"ll solve only first first question.…

Q: The given family of functions is the general solution of the differential equation on the indicated…

A: We have to find the general solution of given DE by given family of function.

Q: Find a set of parametric equations for the line passing through the point (7, 0, 2) that is parallel…

A: We are asked to find the equation of the line.

Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing.…

A: increasing and decreasing intervals of fucntion  fx=3x4 − 4x3 − 12x2 + 5

Q: Consider the figures below. (1) 2- 14 (2) 4- O Continually increase the height of all rectangles. O…

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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.

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

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Q: Use the functions below to find the given value. f(x) = x - 2 g(x) = x² | = (1)(₁_ 6+ z_ d)

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

A: We need to find y2.

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (-2, -2, 0)

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: This question is related to implicit differentiation, We will solve it using given information.

Q: Evaluate the integral. (Use C for the constant of integration.) s¯¹(x) dx COS

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Q: Use Green's Theorem to evaluate the line integral Icov for the given path. (y-x) dx + (2x - y) dy C:…

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Q: Let g(x) = x¹/3√1-2x. Select all of the following values of x in the domain of g where g is not…

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Q: Let - fot² Find the average value of f on the interval [0, 1]. f(x) = dt.

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Q: and the partial fraction decomposition. -2x-9 2 x -3x -2x - 9 2 X - 3x - SERT 0

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Q: Find the general solution of the given second-order differential equation. 3y" + 2y' + y = 0 y(x) =

A: We need to find general solution.

Q: Three different forces act on an object. They are: F₁ (8,5) (1,7) F₂ F3 (0, 3) = - = Find the net…

A: The three forces are given as: F1→=8,-5 F2→=1,7 F3→=0,3

Q: 3X y 2y = 4y + 8y = 2³x + 8x² 2X <-2X Ans: y = ₁2x + ₂xe + cze -25 X -3X 2 —=== ² + x + x + 1²/2

A: This is a problem related to ODE. Based on the general formula and concept we will answer.

Q: lim n→∞ - 17n + 11 11"

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Q: Solve the following system of equations. 3x+4y = 4 6x+4y = 16

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Q: Find the derivative of the function using Chain Rule. Given f(x)=(x²+x-3)√√x²+x-3

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Q: Find ||FI|. F(x, y) = i + j Sketch several representative vectors in the vector field. y O O -4 -2…

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Q: Determine whether the given set of functions is linearly independent on the interval (-∞, ∞o). f₁(x)…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) Jx x5/2 In(x) dx

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Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

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Q: 8 -6 4 수 +

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Q: Evaluate. limx---> 0 tan x - x/ x^3 show the steps in paper

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Q: Find Magnitude and Direction (Angle) Giving the Vector Given the vector u = -47 +17, find the…

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