Find the Taylor approximations of order two for the following functions: The CES production function with kapital K and labour L: Q(K, L) = (K−¹1/4 + L-¹/4) −² at (K, L) = (1, 1).

Q: 8 2. a) Differentiate the function Q(p) = -2³√/p³ (e²-√³) b) Hence or otherwise, determine Q'(1).

A: The given function

Q: 4

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Q: So 0 xe- dư x²

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A: The given rectangular coordinate isSo here we have,

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Q: If 5x² + 3x + xy = 2 and y(2) = 12, find y' (2) by implicit differentiation.

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Q: Find two other pair of polar coordinates one with r>0 and r<0 for  (6,π/4) (-5,3π/2) (3,-π/3)

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Q: find the derivative a. f(x) = (x-1)^3 / x(x+3)^4 b. [(x^2-1)^5-x]^3

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Q: b. List any critical values. c. Identify intervals of increase. d. Identify intervals of decrease.

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: The function f(x) = (4x + 7)e X = 3x has one critical number. Find it.

A: To find the critical number of the function .

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Q: If tan0 = 11/9 and cos 0 > 0, then without finding the angle, find the exact answers to the…

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Q: The region bounded by the curve y = √x, the x-axis, and the line x = 4 is revolved about the y-axis…

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Q: Least squares approximation is a method for finding the line with minimum vertical distance from a…

A: Solution is following in explanation step.

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Q: Consider the function f(x) 2x²10x + 11, 0 ≤ x ≤ 7. The absolute maximum of f(x) (on the given…

A: Given that the function, we have to find the absolute maximum and absolute minimum value

Q: Consider the function f(x) = x¹ - 18x²+2, -2 ≤x≤ The absolute maximum of f(x) (on the given…

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Q: Solve 11 (ex) ¹¹e13 + 6x = 4 5In (3) 17 5 In(3) +- In(3)- 19 11 243 13 17 13 6 +5 In(3)

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Q: If cos 22.5° = √A + √B, then, by using a half-angle formula, find A B =

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Q: The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the…

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Q: Use the graph shown to find the following. (a) The domain and range of the function (b) The…

A: As we can see from the graph, the vertical asymptote is: x=1So the domain is

Q: 8. Graph the = function. 7 if x < 2 3 ₁ifx= 2 2х=3 if *72 piecewise 2x-3

A: To graph the given function, find some points on the curve, plot them on a graph and draw a straight…

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: Differentiate the following function. f(x)=9-4x+5ex f'(x) =

A: Given,

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Q: ∞ Write out the first few terms of the series Σ n=0 3 on (-1)^ 57 What is the series' sum?

A: Formula for sum of infinite G.P. = a/(1-r) Where, a = first term r = common ratio

Q: 5 Solve, y 4 < 0.001 (report with decimals)

A: |y-4|&lt;0.001

Q: x² For the given cost function C(x) = 128√√x + find 42875 the following. For average and marginal…

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Q: Test the series below for convergence using the Ratio Test. n4 0.82 n=1 The limit of the ratio test…

A: The power series is given byRatio test:

Q: What is a Laplace transform of 6sin5t

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Q: (a) What is the equation of the plane passing through the points (1, 0, 0), (0, 3, 0), and (0, 0,…

A: We find a) The equation of the plane passing through the points (1, 0, 0), (0, 3, 0), and (0,0,4).b)…

Q: Test the series below for convergence using the Ratio Test. Ë n=1 3n n! The limit of the ratio test…

A: The power series is given byCriteria of Ratio TestIf 1, The series diverges end text text L

Q: (4) A closed rectangular container with a square base is to have a volume of 2250in². for the top…

A: A closed rectangular container with a square base is to have a volume of 2250 in3. The material for…

Q: 1) Find the general solution of the following differential equation y" - 6y +9y = 0

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Q: Practice 1: If tan y = x where sec² y write X 1300 (1) in terms of

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Q: Determine if the geometric series converges or diverges. If it converges, find its sum. 3 8 0·00 + +…

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Q: Find any relative extrema of the function. List each extremum along with the x-value at which it…

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Q: Find the indicated maximum or minimum value of the objective function in the linear programming…

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Q: The manager of a 100-unit apartment complex knows from experience that all units will be occupied if…

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Q: 13. Σ n-2 -1. In n

A: Given a series  thenThe given series is convergent if p&gt;1The given series is divergent if

Q: Write S = Σ n=5 SN = S = 1 n(n-1) as a telescoping series and find its sum.

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Q: At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 21 knots and ship…

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Q: The police radar reads that the distance between the police car and the red car is decreasing at a…

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Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

A: To find the critical points of the following function. By using the Second DerivativeTest to…