4) A manufacturer has determined that the total cost C of operating a factory is C = 0.5x^2 + 15x + 5000 , where x is the number of units produced. At what level of production will the average cost per unit (C/x) be minimized? Topic- critical points and applications

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A: The objective of the question is choose the correct option that is a open set.

Q: → → If m= (2. 1. 5) and n = (3. 0. x) are perpendicular, then the value of x is

A: Solve the following

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A: Expand log series

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Q: дz For z = x² + xy³ ; x = uv² + w², y = u + vew, find when u = 2, v = 1, and w=0 Əw

A: z=x2xy3, x=uv2+w2, y=u+ve2at u=2, v=1 and w=0, x=2×12+0=2y=2+1e0=2

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A: To find the area of the region bounded by given curves.

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Q: y = 2x2 + 9; (a) x = -1 (b) x = 0 (c) x = 1 dx dt of the given function at the rate dx/dt. Find…

A: We have to find out the derivative

Q: 4 Find the general Solution of the following PDES • з Их + 2 Иу -Х u(x,c) =4е 2 (зу-2х)12 ans3- и(x,…

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Q: 9) Two apartment tenants have a total of 600 feet of fencing to enclose a rectangular garden and…

A: Please refer to the image below

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A: Let's find average value of given function.

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A: Basic identities of integration are used

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Q: Solve Zxy and Zyx when Z=2xy³ − 3x²y

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Q: Given 0 t² | s² solve for 20 at

A: Given: θ=st2-ts2   As we know that; The Sum/Difference Rule: f±g'=f'±g' The Power Law: ddxxn=nxn-1…

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Q: derivative of y = e(sin⁡x) − sin⁡(ex)8

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Q: 2 . show that V(x,y) = x 'f (2x+y) is the general Solution of: av X du 2X 1 = V ду dx

A: To show that, vx, y=x f2x+y is the general solution of: x∂v∂x-2x∂v∂y=v

Q: f(x) = 4√x + 2x1/2 – 8x-7/8 + x2 1 23 +2

A:

Q: In y = C₁e* + C₂е¯x

A: Given problem:- Find its differential equation through eliminating arbitrary constants.    In(y) =…

Q: Problem 4. (. Let C be the curve given by parametric equations r(t) = 1², y(t) = 2t, z(t) = ln t, t€…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: SET-UP a triple integral that will solve for the volume inside the sphere x² + y² + z² = 2z and…

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Q: 1ln(1 + x) dx X 0

A: We have to integrate

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Q: Set up the triple integral that will give the following: : 0≤ x ≤ 1,0 ≤ y ≤ (a) the volume of R…

A: Given

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A: To find f(x+h) replace x by x+h in f(x).

Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², y(t) = 2t, z(t) = lnt, t€…

A: To find equation of tangent line and then arc length of thegivencurve.

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Q: Given the points P(2, 1, 1), (0, 4, 1), R(-2, 1, 4) and S(1,5,-4)

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Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², y(t) = 2t, z(t) = lnt, t€…

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Q: writing the given quadratic s^2 +6s + 10 in the form (s+a)^2 + B^2 (that is to complete the square).…

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Q: Evaluate the double integral: L y 1/3 27 +1 dx dy.

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Q: As shown in the required readings or videos find the general solution to the differential equation…

A: Here we have to find the general solution of the given differential equation,  y'+2y=2ex…

Q: particular

A: