Consider the Cobb-Douglas Production function: P(L, K) = 28L0.5 -0.5 Find the marginal productivity of labor and marginal productivity of capital when 12 units of labor and 16 units of capital are invested. Give your answers to at least 4 decimal places if necessary. Marginal Productivity of Labor when L is 12 and K is 16 = P₁(12, 16) = Marginal Productivity of Capital when L is 12 and K is 16 = PK(12, 16) - =

Q: The DE M(x,y) dx + (3e-4x + 7y) dy=0 is an exact differential equation if O M(x,y)=-12ye-4x-8y O…

A:

Q: Ət A. Use the chain rule to find and as functions of x, y, s and t. Ət = მა Suppose z = = B. Find…

A:

Q: Show algebraically where the tangent line of the function r=1+cos theta is vertical and where the…

A:

Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = 27 - x, y…

A:

Q: The region bounded by f(x) = 0, and y = 0 is rotated about the y-axis. Find the volume of the solid…

A:

Q: Find dy/dx.  y=7x

A: Use the basic result of differentiation.

Q: Use a triple integral to find the volume of the given solid. The solid enclosed by the paraboloids y…

A: solid is enclosed by the curve y=x2+z2   , y=72-x2-z2

Q: WORK PROBLEMS (. You need to provide a clear and detailed solution for the following Questions: )…

A: This question is related to vectors, we will solve it using given information.

Q: dy/dt = 2.5. 9. Given y = e2x+1, find dy/dt when x = 4 and dx/dt = 0.5. 3r C: (d when x = ? and

A:

Q: (x) x + 1/2 Ax² + Bx + C (x² + D)²

A: Topic:- application of derivatives

Q: 1) If f₁ ln x dx = 1 and ₁² lnx dx = 1+e² then fe² lnx dx = a) e² b) 2+ e² c) -e² d) −2+ e²

A: If ∫1eln x dx=1 and ∫1e2ln x dx=1+e2 then to determine the vaue of ∫ee2ln x dx.

Q: 9. f 6 sec¹ xdx

A:

Q: Find the local and/or absolute maxima and minima for the function over the specified domain: y=x+1|…

A:

Q: Find the Taylor polynomial p3(x) for f(x) = 5x¹/³ at x = 3.

A:

Q: A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is…

A:

Q: Find the vertex, focus, and directrix of the parabola. x² = 6y vertex focus directrix (x, y) (x, y)…

A:

Q: Suppose f(x, y) = xe 2-32². Answer the following. 1. Find the local maxima of f. List your answers…

A:

Q: The position of a particle moving along a coordinate line is s=root 28+4t​, with s in meters and t…

A:

Q: Sketch the curve of the following: y = x5/3 - 5x2/3

A:

Q: Using a proper substitution, Bernoulli's equation dy dx - 5 xy = - 4x²y4 will be reduced to the…

A:

Q: Which graph is a possible sketch of the function f(x) = (x-6)(x+3)³ ? 625 500 375 + 250 125 +…

A:

Q: 3. f cos¹ 20d0

A: We know, ∫cosnxdx=(cos(n-1)x*sinx)/n + (n-1)/n ∫cos(n-2)xdx

Q: Suppose f(x,y) = = tan(x) + y and u is the unit vector in the direction of (-3,-1). Then, a) ▼ f(x,…

A:

Q: Let u₁ = 0 -6 -4 0 A. The vector , U₂ = Select all of the vectors that are in the span of {u₁, U₂,…

A: We have to select the vectors that are  in the given span.

Q: Differentiate. y' = || y = eP(p + p√p) X

A:

Q: 1. A bacteria culture initially contains 2000 bacteria and grows exponentially. After 3 hours, there…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the equation of the tangent line to y 32²—6x+1, at x = 2.

A:

Q: For the function, do the following. 1 f(x) = 2x from a = 2 to b = 3 Approximate the area under the…

A:

Q: Find all values of y such that the distance between  (9,y) and (-4,6) is 15. y= ?

A: We know Distance formula= x2-x12+y2-y12

Q: Question Find the Maclaurin polynomial på (x) for f(x) = 5ª. Provide your answer below:

A:

Q: Find the critical points in the domain of the function: y=tan(x) . If there are no critical points,…

A:

Q: Use the power series f(x) = 1 + x n=0 to determine a power series for the function, centered at 0,…

A:

Q: Describe how the graph of can be obtained from f(x) = x². 7 g(x) = (x + 2)²-3 The graph of g(x) is…

A:

Q: Find all the first and second order partial derivatives of f(x, y) = -7 sin(2x + y) + 5 cos(x - y).…

A:

Q: Let A = {Dirk, Johan, Frans, Sarie}, B = {Frans, Sarie, Tina, Klaas, Henrika), C = {Hans, Frans).…

A: A=Dirk, Johan, Frans, SarieB= Frans, Sarie, Tina, Klaas, HenrikaC=Hans,  Frans

Q: Question 1. equation : : Consider the differential y cost + 2te³ + (sin t + t²e³ − 1)y' = 0. - a)…

A:

Q: Determine whether the statement is true or false. (ln x)4 = 4 ln x for all x in (0, ∞). True False

A:

Q: Determine whether the improper integral converges or diverges, and if it converges, find its value.…

A:

Q: Consider the Initial Value Problem: y' = −2√y + 3x³ + 4, _y(2) = 5. In order to use Euler's method…

A: we have given h=0.1

Q: Calculate all four second-order partial derivatives of f(x, y) = 2x²y + 4xy³. = || = )= ||

A:

Q: Find f'(a). f'(a) = f(t) 6t + 2 t + 3

A: As per the instruction, we will be answering the first question. Given: Now,         f'(t)=6t+2t+3'…

Q: INSTRUCTIONS: Differentiate with respect to g(x) = ln(x√x² - 1)

A: according to bartleby guideline we do only first part g(x)=lnxx2-1d…

Q: d dx f(x) = ex, f(0) = 8.

A:

Q: (7 y² +6 x)dx+ 11 x y dy=0 (*) a) Determine whether the given differential equation (*) is exact…

A: We have to determine whether the given differential equation (*) is exact

Q: Find dy/dx. y=x0.75

A:

Q: 5. sin³0 cos-20d0

A:

Q: 1. Consider a polynomial function f(x) = co + c₁x + c₂x² + ... + Cd-1d-1 + card. A. Applying the…

A:

Q: Suppose Find the value of f(82). f(82) = dx f(x) = 10, f(0) = 22.

A: I am attaching image so that you understand each and every step.

Q: Evaluate the repeated integral: a) 0 12 e² - 12 e b) 06 c) 0 24 d) 12 e) 0 24 e² - 24 e f) O None of…

A: We need to find the value of ∫-11∫1y-2∫ee23x+3yzdzdxdy

Q: ind the intervals on which f is increasing or decreasing. Find the local maximum and minimum values…

A: