Use Lagrange multipliers to find the indicated extrema, assuming that x, and y are positive. Minimize f(x, y) = x² - 10x + y² - 14y + 28 Constraint: x + y = 6 7 =

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

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Q: Sales Analysis The total sales S (in thousands) of a video game are given by at² t² + b' where a =…

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Q: The total cost (in dollars) of manufacturing x auto body frames is C(x) = 50,000 + 700x. (A) Find…

A: The total cost of manufacturing x auto body frames is Cx=50,000+700x

Q: 4 3 dy = (y² + 1) cos(x) y dx хр

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Q: Find the areas of the regions enclosed by the following curves. (a) r = 1+2cosł

A: Given curve, r=1+2cos(θ) For range let r=1+2cos(θ)=02cos(θ)=-1cos(θ)=-12⇒θ=2π3

Q: Find the general solution of the following differential equat 121y" - 4y = 0 NOTE: Use c₁ and c₂ as…

A: Given: 121y''-4y=0

Q: 7/5 Find f'(x) if f(x)=9x5-5x² + 10000. O A. f'(x) = 63x6/5 - 10x 6/5 B. f'(x) = 63³x6 O c. f'(x) =…

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Q: You purchase a 50# case of potatoes. Once peeled, you are left with 35# of usable product. What is…

A: You purchase a 50 case of potatoes.Once peeled, you are left with 35 of usable product.

Q: 11. Find the linear approximation of f(x) = √√x_ at a = 1. Use the linearization to estimate the…

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Q: Find a center of mass of a thin plate of density 8 = 6 bounded by the lines y=x and x = 0 and the…

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Q: Find c such that f(c) equals the average value of f(x) = 4x + 6 over [-7, -2]. Provide your answer…

A: Given: f(x)=4x+6

Q: Find the points of inflection of the graph of the function. (If an answer does not exist, enter…

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Q: Find the area of the surface obtained by rotating the curve about the y-axis. = (y² - Iny), 1 ≤ y ≤…

A: surface area  about  y axis  bounded by  x=g(y)Area=∫ab 2π g(y)1+g'(y)2  dy

Q: Consider the following. y = x² y = 12 - x K 16 14 12 -2 10 B 6 4 2 2 8 10 12 (a) Find the area of…

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Q: Are the partial derivatives and gradients of a function the same, no matter your starting position?

A: Topic:- application of derivatives

Q: Find the minimum distance from the point to the plane x - y + z = 6. (Hint: To simplify the…

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Q: Express your final answer at least three (3)decimal places. The population of a townin…

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

A: Given that , fx,y,z=x2+y2+z2 and constraint is x+y+z-27=0 find the extrema using Lagrange…

Q: A car sharing service offers a membership plan with a $40 per month fee that includes 10 hours of…

A: Cost of membership plan = $40 Let No.of driving hours = x

Q: Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient…

A: Here we have to choose the correct option.

Q: Find the area of the shaded region shown in the graph. The area of the shaded region is (Type an…

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Q: Evaluate the limit 1-04 me 1 Amar lim 3 +3) x+1 x+3 Una

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Q: h(x, y) = x²7xy - y² relative minimum relative maximum saddle point (x, y, z) = (x, y, z) = (x, y,…

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Q: 10. Find the limit (if it exists) of the sequence (x_n) where x_n= cos(n)/n.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

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Q: Complete the input-output table for f(x) = X -4 -3 -2 -1 -0.5 -0.25 0.25 0.5 1 2 3 4 5 X 5 -. If…

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Q: Evaluate the integral. (Assume a b. Remember to use absolute values where appropriate. Use C for the…

A: Given ∫4(x+a)(x+b)dxTo evaluate the integral:

Q: Find the solution of the given initial value problem 50y" + 15y"+y' = 0, y(0) = -2, y'(0) = -10,…

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Q: X Find the average value of y= 4 cos on I 2 ST 6

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Q: 1. y" - 2y' - 3y = 5e¹, y(0) = 1, y'(0) = 0 2. y" + 2y + 5y = 3 sin(2x) 3. y" - 4y + 4y = -7x+4x²,…

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

Q: Use any method to determine if the series converges or diverges. Give reasons for you! M8 n=1 Select…

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Q: The piecewise function f(x) is graphed below. Use the graph to find the average value of the…

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Q: Identify the symmetries of the curve r=7+7 cos 8. Then sketch the curve. Is the curve symmetric…

A: see below the figure and answers

Q: 15 Find the Equation of the tangent at (); 4 2 'V or to armist mi Y sin (127) = x cos (24) 7 ition]…

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Q: 1. Find the numbers for x where the function below is not continuous. Explain what type of…

A: We can find discontinuity of the function .

Q: For the given functions f(x) = − 9x², g(x) (1) (fog)(x) = (2) (gof)(x) = (3) (ƒ ○ ƒ)(x) = (4)…

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Q: For the two 3 x 3 matrices A and B with det(A) = -3 and det(B) = 2, Select one: O True O False det…

A: Given :mx+3y-z=m    2x+z=1              -2x-3y+mz=0  detA=-3detB=2

Q: Alexandra invested $1,100 at the end of every month into an investment fund that was earning…

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Q: The piecewise function f(x) is graphed below. Use geometric formulas to evaluate the following…

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Q: Use the given graph of the function to find the function information. (A) Intercepts (B) Vertex (C)…

A: given function is a parabola for reference

Q: ese²x Evaluate Cotx 3. dx

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Q: Find all relative extrema and saddle points of the function. Use the Second Partials Test where…

A: we will use second partial test.

Q: Find the solution of the given initial value problem. 5y""+65y-580y = 0; 11, y'(0) = 31, y"(0) =…

A: A detailed solution is given below.

Q: aunauna Question 2 of 10 al a) Given the following piecewise function, evaluate each limit below:…

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Q: dx sin² x cos²x 10. The value of f; A sinx-cosx+C B. cos x– sin x+C C. tanx-cotx+C D. cotx-tan x + C

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Q: doesn't

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Q: Find the derivative of the function y = arctanx + 1+x²

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Q: Find y ay ax Y = (x²+1) • In (x² + 1) if

A: We know that derivatives power rule is  d(xn)/dx = nxn-1. And also know that: d(lnx)/dx = 1/x.…

Q: Find the surface integral of the field F(x,y,z)=9xi +9yj +9zk across the portion of the sphere x² +…

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Q: Evaluate the integral [x Select one: O Inx+C O O 3 O None of them O O - 3 X 3 xả ln xdx Inx-+C 3 с 3…

A: Here is the solution: