Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, y, z) = x2 + y2 + z2;  x4 + y4 +z4 = 11

Q: Find the extreme values of f subject to both constraints. f(x, y, z) = yz + xy;  xy =1;  y2 + z2 =…

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Q: Find the particular solution of the differential equation that satisfies the initial condition.…

A: The given differential equation .The aim is to find the solution to the differential equation that…

Q: Prove that: ((x-(x))²) = (x²) - (x) ²

A: As per the guidelines I am supposed to solve one question at a time. Please repost the other…

Q: 8) Sketch the graph of the polynomial function: f(x) = x²(x + 4)(x − 7)*(x − 2)³

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Q: Find the absolute maximum and minimum values of f on the set D. f(x,y) = 2x3 + y4 + 1,  D = {(x,y)|…

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Q: -5-4-3-2 X 5 4 3 2 1 -2 -3 -4 -5- 1 2 List all the numbers x at which the function graphed above is…

A: since you have posted multiple question which are not interlinked so i have solved first question as…

Q: Find the derivative of the following function using the Fundamental Theorem of Calculus. F'(x) =…

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Q: To find the surface area of of revolution, we need to make two decisions: S = √2πz i) Shall we use S…

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Q: Differentiate the function.  y=(5x-5)^2(4-x^3)^2

A: Given,

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Q: Sketch the region bounded by the curves y = 3 − x 2 and the line y = 2x, and find the area of the…

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Q: Use the graph to state the absolute and local maximum and minimum values of the function. (Assume…

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Q: Let e denote the ellipsoid and let L denote the plane 4² = 1 12x + 8y +9z = 51. Using Lagrange…

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Q: Find the velocity and position vectors of a particle that has the given acceleration and the given…

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Q: A hemispherical dome of radius 20 feet is to be given 11 coats of paint, each of which is 1/100 inch…

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Q: Consider the plane with equation x + 2y + 2z - 60. Determine the point on the plane that is closest…

A: The given plane is,Compare this equation with So here we have,

Q: You are told that f(x) is everywhere continuous, passes through the point (6,3) and f(x) +3 x-4 It…

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Q: Use the graph to determine the equation of the vertical asymptote: -5 -4 -3 -2 -1 X || 5- 4 3 2 7 -1…

A: Here the given graph is,we have to find the vertical asymptote.

Q: Use the change-of-base formula and a calculator to evaluate the logarithm. Round your answer to…

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Q: 1. If h(x) = xf(x) + 4g(x) then, h'(1) 2. If h(x) f(x) g(x) 3. If h(x) = 2x + f(x)g(x) then, h'(3) =…

A: x1234f(x)42410g(x)-20216f'(x)-4048g'(x)60624

Q: Computek(k+1) k=1 Hint: Use the fact that Ek-1(ak-ak-1)= anao (this is called telescoping) and…

A: The given series .The aim is to compute the sum of the series.

Q: 4. Find the limits (a) lim x-1 (b) lim x-0 xª+¹(ln x + 1) − x 1-x ((² + 2)1/²) 1/². e

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Q: Find d²y 2 dx 11 y=¹1√√x

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Q: The letters A through E on the graph represent different time intervals. Use thom letters to answer…

A: Solve the following questions using graph.

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Q: 1 (x³ +1) ³ x³ dx

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Q: nd [₁9(a) d g(x) dx = -10, evaluate the integral If g(1) = -4, g(5) = -4, and [₁²xg' xg'(x) dx.

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Q: hat value of the constant c is the function f defined below continuous on (-00,00)? f(1) = Jr² - c…

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Q: Consider the following statement. For all sets A and B, (A U BC) - B = (A - B)U BC. An algebraic…

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Q: Write the expression as a sum and/or difference of logarithms. Express powers as factors. In…

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Q: Find the indefinite integral. [cxc² (7) ax CSC dx Step 1 Observe that 1/3 1/3 is the derivative of…

A: .

Q: 5. (a) (b) If 5+3x g(x) = x-3 What is the domain of g(x)? Verify (with a sketch and/or short…

A: The given function is

Q: Find the slope of the graph of the function at the given point. f(x) = √8 - x³, (-2,4) f'(-2) =

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Q: 4. Let g (a) = f(t) dt. where f is the function whose graph is shown. a. Use Part 1 of the…

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Q: Use any method to evaluate the integral. S- 22 dx (121x² + 1)²

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Q: Find r(t) for the given conditions. r'(t) = 8e4ti +5etj, r(t) = 2(et)i+5e¹j 4t X r(0) = 2i

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Q: The differentiable functions f and g are defined for all real numbers x. Values of f, f', g, and g'…

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Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. S…

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Q: Find the critical numbers of the function. g(t) = t√13-t, t < 12

A: To find the critical numbers of the following function.

Q: If we apply Rolle's Theorem to the function f(x) = 2x² - 16x -9 on the interval [2, 6], how many…

A: We will use the concept of Roll's theorem and using this we will solve it.

Q: Describe the left-hand and right-hand behavior of the graph of the polynomial function. (Select all…

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Q: Consider the following function. Use a graphing utility to confirm your answers for parts (a)…

A: In this question, we will find critical point , Increasing or decreasing interval and Relative…

Q: Use the information to find and compare Ay and dy. (Round your answers to three decimal places.)…

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Q: vertice (0,e) and (6,2) asymptotes y = ax and y=4-22 The Standard form of Hyperbola is; with…

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Q: y = (sin¯¯¹(x²)) tan-¹.

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Q: If f(y) = cos-¹(3y¹), find f'(y). Use exact values. f'(y) = =

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: b) x+2 4 x-2 6 = 2x-1 3

A: Given,

Q: Use Lagrange multipliers to find the extreme values of the function subject to the given constaint.…

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Q: Complete the table by identifying u and du for the integral. [r(g(x))g(x) dx [ (tan(x))² (sec(x))²…

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