urgently 3. Output, P, is produced using two inputs, K and L, according toP= f(K, L) = 2 +KL-251) Find the equation of the tangent plane to the production surface at the point corresponding to K = 4and L = 3.2) What is the equation of the tangent plane to the level curve corresponding to P = 4 at (K, L) = (4,3)?3) What is the Marginal Rate of Substitution (MRS) of L for K along the level curve corresponding toP = f(4; 3) at (K, L) = (4:3).

Answered: Image /qna-images/answer/5da17eb0-c0f4-481d-a5d2-6c37a881e3bf.jpg

Answered: 3. Output, P, is produced using two…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Assume that a company's marginal cost function for the manufacture of x phones per hour is c(x) = 180 − 0.006x, and that they sell the phone for an average wholesale price of $520. Use a Riemann sum with n = 5 subdivisions to estimate the total additional hourly profit corresponding to an increase in production and sales from 10,000 to 20,000 phones per hour. (Use a left Riemann sum to find your answer.)
A mass of 1 kgkg is attached to the end of a spring whose restoring force is 180 NmNm. The mass is in a medium that exerts a viscous resistance of 156 NN when the mass has a velocity of 6 msms. The viscous resistance is proportional to the speed of the object. Suppose the spring is stretched 0.07 mm beyond the its natural position and released. Let positive displacements indicate a stretched spring, and suppose that external vibrations act on the mass with a force of 7sin(3t)7sin(3t) NN at time tt seconds. Find an function to express the steady-state component of the object's displacement from the spring's natural position, in mm after tt seconds. (Note: This spring-mass system is not "hanging", so there is no gravitational force included in the model.)
(a) Water is flowing out at the rate of 6 m / min from a reservoir shaped like hemispherical bowl of radius 13 m, shown in Figure Q2 (a). Given that the volume of water in a hemispherical bowl of radius R is V = (?/3) y^2 (3R – y) when water is y meters deep. Determine: (i) rate of the water level changing when water is 8 m deep. (ii) the radius r of the water's surface when the water is y m deep. (iii) rate of the radius r changing when the water is 8 m deep.
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A pulse (gas) travelling along a fine straight uniform tube filled with gas causes the density at any time t and distance x from the origin where the velocity is u\index{0} to become ?\index{0}ϕ(vt-x). Prove that the velocity u (at time t and distance x from the origin) is given by
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Suppose that the Celsiustemperature at the point (x, y) in the xy-plane is T(x, y) = x sin 2yand that distance in the xy-plane is measured in meters. A particleis moving clockwise around the circle of radius 1 m centered at theorigin at the constant rate of 2 m / sec. How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point P(1/2, √3/2)?
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A mass of 1.75 kg is attached to the end of a spring whose restoring force is 100 N/m. The mass is in a medium that exerts a viscous resistance of 15 N when the mass has a velocity of 6 msms. The viscous resistance is proportional to the speed of the object.Suppose the spring is stretched 0.03 mm beyond the its natural position and released. Let positive displacements indicate a stretched spring, and suppose that external vibrations act on the mass with a force of 3sin(2t) NN at time tt seconds.Find an function to express the steady-state component of the object's displacement from the spring's natural position, in mm after tt seconds. (Note: This spring-mass system is not "hanging", so there is no gravitational force included in the model.) Enter exact value for the constants, or 8 decimal places. u(t) =

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