5. For a vcctor Á written in spherical coordinates, A = A,f + A,® + AøØ, the spherical coordinate divergences is 1 (sin 0 Ag) + 1 V·Ã= (r² A,) + r2 dr r sin 0 Ə0 r sin 0 dø What is the Laplacian in spherical coordinates?

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A: We want to find when the marginal cost of the function start to increase.

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A: A detailed solution is given below

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Q: 2. g'-yso ylo)=2 gilo): -2 y'Co)= y'(0)= -2 : -2

A: Given: y''-y=0, y0=2, y'0=-2 So, we can also write as: D2-1y=0   The auxiliary equation is: m2-1=0

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A: here ?∫ dx = 4x + c now we can differentiate both side so we get the function f(x) = 4 so here…

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

A: We will create a Lagrange's function to solve the problem.

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Q: = 4x +C

A: Topic = Integraton

Q: Find the gradient of the function at the given point. w = x tan(y + z), (19, 5, -1)

A: To find the gradient of the function at the given point.

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Q: Which of the following is not a possible zero of f (x)=2x-5x+127

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Q: Which of the following is a solution of the equation 11 · 4* = 7 · 5*? Select one: a. x = 11/7 b. x…

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Q: first principles. (i) x² (ii) e* (ii) log (x+ 1)

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Q: 3. The following curves bounds a certain area: y = 4x – x2 y = 4 and x = -2 Determine that area.

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Q: 33. y" + y' + 2y = 0, y(0) = y'(0) = 0 ||

A: Find your answer below

Q: Solve the First Order Differential Equation using appropriate method. Show complete and detailed…

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A: Here we have to find the equation of a plane.

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Q: dy J 1+y+1

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Q: 67 V3 1 Use De Moivre's Theorem to express the complex number on the form a+ bi. ---1

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Q: Find the derivative. y = e2= . 8x3 24x?e2 + 16x4e2« – 1 O 2e2a . 24x? 24x e2 + 16x³e2* O 2xe2a…

A: We will find the derivative using Chain rule.

Q: Which of the following is not a possible zero of f (x)=2x-5x+12?

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Q: 3 V= ㅠ (x4 – 18x? + 81) dæ 3 18x? = T + 81x n 5 3 [(-0)-(뿌 ) -0) + 18.3 3

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Q: Find the vector component of v = (4, – 1, 7) along b = (3, 6, –6) and the vector component of v…

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

A: Two lines intersect if their corresponding components are equal.

Q: Consider the following IVP: y'' -3y' -10y = 1, y(0) = -1, y'(0) = 2

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Q: 【コxマー52

A: Given problem:- ∫x2x2-53dx

Q: Find an equation of the plane through the origin that is parallel to the plane 5x – 4y + 6z + 10 =…

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Q: dy cos x + (sin æ) y = 9 dx y = 9 sec - C cos æ y = 9 sin a ++ C cos x y = 9 sin? x + C cos æ y = 9…

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Q: lim (5x + х+ 3,

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Q: 3. 8х' + 13 2. S 3 4x' + 8х + х + 2 2

A: integration

Q: 1. * Sx² sin 2x dx -x²cos2x ¸ x sin 2x , cos 2x +C 8. –x²cos2x x sin 2x , cos 2x + C A 2 2 B…

A: To Find : ∫x2sin(2x)dx

Q: Find the area bounded by the graphs of f(x)=x+2,g(x)=3x²+5 , x=-1 and x=1.

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Q: If g(2) = 3 and g'(2) = 1 and f(x) = [g(x)]°, find f'(2) %3D

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Q: Given the following function. - if x2 x > 2 x-2 5, if x = 0 or x = 2 Can f continuous at (-1, ∞)?…

A: Here, for the given function: limx→0-f(x)=limx→01x1+x-1x  (∞-∞…

Q: Find all the local maximum and minimum and saddle points, with their values, for the function f(x,…

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Q: Find the area bounded by the curves f(x)=x+8 and g(x)=x²-x.

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Q: i. Comment whether the sequence is Converges or diverges. ii. Obtain the first five terms of that…

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Q: 5-(1+x')(dy-dx)= 2.xydx;

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Q: Use the quotient rule to find the derivative of 8e" + 4 - 9x7 + 9x° Use e^x for e". You do not need…

A: We will find the derivative.

Q: Given the cost function for a product: C(q) = -0.00932q + 0.196q? + 1.43q + 36, at what level of…

A: Find your answer below

Q: The demand function for a particular pair of sunglasses is p = 135 – 0.095q. (a) If the sunglasses…

A: The given demand function for a particular pair of sunglasses is: p=135-0.095q...(1) where q is the…