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## Related Calculus Q&A

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Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

Q: If z-f (x y): then its total differential can be expressed as * (),中 (). dyds dy + dz O Option 2 O…

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Q: If x2 + y2 = 25 and dx/dt = -2, then what is dy/dt when x = 3 and y = -4.

A: Differentiate both sides with respect to t.

Q: Suppose a particular investor derives utility function - U(x, y) - from owning x units of stocks and…

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Q: Suppose 4x + 9y - 25, where x and y are functions of t. (a) If dy/dt-, find dx/dt when x = 2 and y =…

A: Given: 4x2+9y2=25 Since, x and y are functions of t, therefore differentiating each sides with…

Q: If x^2 + y^2 = 25 and dx/dt = -2, then what is dy/dt when x =3 and y = -4

A: Given that x2 + y2 = 25 .... (1) dx/dt = - 2 To find dy/dt when x =3, y = - 4

Q: dz Suppose that z = f(x, y) is differentiable at the point (8, 16) with f,(8, 16) = 3 and f, (8, 16)…

A: Click to see the answer

Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: See the attachment

Q: |(a) Suppose a particular investor derives utility function - U(x,y) - from owning x units of stocks…

A: Click to see the answer

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Q: 11. Show that the function 2ry when r + y + 0 h(r, y) = 0; when r = y = 0 has partial derivatives…

A: Given: h(x,y) =2xyx2+y2; when x2+y2≠00 ; when x=y=0 To show that the partial derivative…

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Q: Suppose that a duck is swimr - perature is given by the formı v²sin x. Find dT/dt in two chain rule…

A: Given query is to find the derivative of function T.

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Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 7y + 3z) at the point (– 2, – 3, – 6). - -

A: Click to see the answer

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Q: A particle moves on the circle x2+y2=25 in the xy-plane for time t≥0. At the time when the particle…

A: Given x2+y2=25 Point (3,4), dxdt=6

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Q: A particle moves on the circle x2+y2=25 in the xy-plane for time t≥0. At the time when the particle…

A: Click to see the answer

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Q: SM 6. Suppose that f (x, y) has continuous partial derivatives. Suppose too that the maximum direc-…

A: Theorem: Let fx, y be a function with continuous partial derivatives. The maximum value of the…

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Q: Compute the differential dz of the function. z = x*y" ,7,,11 dz

A: Click to see the answer

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Q: Find fz and fy- f(z, 9) = [" 9eª dt f.(x, y) = f,(x, y) =

A: Click to see the answer

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Q: 3. Find the total differential of z = f (x, y) if z2 - y = (1- 2x)z.

A: Given: z = f(x,y) such that z2 - y = (1-2x) z To find: Total differential of z = dz

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Q: The time rate of change of liquid circulating in two tanks is govemed by dy -0.02x + 0.02y, = 0.02x…

A: Click to see the answer

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Q: Assume that x and y are differentiable functions of t. Find dx/dt given that x= -3 , y= -2 , and…

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Q: 8. What is the relationship between a and b so that F(x, y) = (ary, 3ax + bry) is source free?

A: That's easy. Have a great day!!!

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Q: Find the value of dx at the point (1,1,1) if the equation 6xy + z"x-2yz = 5 defines z as a function…

A: Given: (x,y,z)=(1,1,1) and z=6xy+z4x-2yz-5=0

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Q: Find a function w = ƒ(x, y) whose first partial derivatives are ∂w/∂x = 1 + ex cos y and ∂w/∂y = 2y…

A: Click to see the answer

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Q: 3. Find the total differential of z = f(x, y) if z2 - y = (1– 2x)z.

A: Total differential of a function z=fx,y is dz=∂z∂xdx+∂z∂ydy

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Q: (a) Solve for the initial value problem by using Laplace transforms method у"- у'- бу %3DSin 2t y(0)…

A: Click to see the answer

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Q: Find the partial derivative at point(u,v)=(-4,0) of w=ln(xa+yb+za),x=uevsin u y=uevcos u, z=uev,…

A: Click to see the answer

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Q: 3. Evaluate the gradient of S(1, y, 2) = In(cosh z+ y) - arctan| at (1,y) = (7/2, 1).

A: Given that fx,y,z=lncosh x+y-z2 arctanx2y2+z2 To find the gradient of f(x,y,z) :…

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Q: dz Suppose that z = f(x, y) is differentiable at the point (32, 8) withf,(32, 8) = 4 and f, (32, 8)…

A: Click to see the answer

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Q: Some diseases (such as typhoid fever) are spread largely by carriers, individuals who can transmit…

A: Solution.

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Q: 2. Find the linearization of the function f(x, y) = In(x³y®) at the point (xo, yo) (4, 3). Leave all…

A: Consider the following function: fx,y=lnx3y6 fxx,y=ddxlnx3y6=1x3y6×3x2y6=3x…

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Q: 4. Given xy+x*y=2 such that d/dt =2 in/sec. Find dy/dt for x= 1

A: Click to see the answer

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Q: Compute the differential dy for y = -6x° + 8x5. dy =

A: topic - differential equations

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Q: Can i get help step by step please

A: To find dx/dt when y = 2 and dy/dt = 5

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Q: Compute the differential dz of the function. 3,,10 x°Y %3| dz

A: Click to see the answer

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Q: If f(x, y, z) = 16xy – 4yz – 4zx + 3, then the first order partial derivative fz = - - (4y + 4x) - –…

A: When a function is differentiated concerning a particular variable and the rest all the variables…

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Q: find ∇f at the given point. ƒ(x, y, z) = x2 + y2 - 2z2 + z ln x, (1, 1, 1)

A: The gradient of a vector f is the collection of all it's partial derivatives. It is denoted as ∇f.

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Q: find ∇f at the given point. ƒ(x, y, z) = x2 + y2 - 2z2 + z ln x, (1, 1, 1)

A: Given function is fx,y,z=x2+y2-2z2+zlnx and point=1,1,1

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Q: Find the partial derivative of f(x,y) with respect to y at the point (3,2) f(x,y) = ln(x^2y-xy^2)

A: A partial derivative of a function of several variables is its derivative with respect to one of…

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Q: Find the value of at the point (1,1,1) if the equation 3xy +z°x-2yz = 2 defines z as a function of…

A: First do the partial differential in both the sides and then separate ∂z∂x and then put the value…

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Q: From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)

A: Click to see the answer

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Q: 1. Suppose y = f(x) and that x is changing over time. How is dy/dt related to dx/dt?

A: Given that: y=f(x)

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Q: 4. Given that c(t) = t² + 2, y(t) = t³ – 2t and f(x,y) = x² sin (xy). Using the df and evaluate it…

A: Click to see the answer

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Q: tan x cotx 1 -dt+ dt%3D1 1+ t? t(1+ f) 1/e Ve prove LHSIS equal to RHS

A: Note ÷ I have used logarithm formula many times 1)ln(a/b)=lna - lnb 2)ln ab = b ln a

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y – 4xyz + 6yz²…

A: Given f(x,y,z) = 2x²y - 4xyz + 6yz²

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Q: fy = f(r), how do we define the differential dy

A: Click to see the answer

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Q: 6,3 + 4x°y +5. 5. 2 Find the first partial derivatives of f(x, y) = 5x°y° + 4x°y +5. af dx II

A: Given: fx, y=5x6y3+4x5y2+5 To Find: ∂f∂x=?

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Q: a)Let z = x?y – y² where x = t2 and y = 2t . Find dz/dt at t=1 using chain rule.

A: Given query is to find derivative is nge chain rule.

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Q: Suppose X1,..., Xn are iid with pdf f(r; 0) - 0<r<8, zero elsewhere, find: (a) The mle 6 for 0. Then…

A: Except the first line, all steps and conclusions are correct, even in first line, the conclusion for…

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Q: (a) x = t* - t + 1, y = t2 Select--- v (b) x = 2 - 2t, y = VE --Select--- v (c) x = sin(2t), y =…

A: Match the graph with their parametric equations.

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 9xyz + 10yz²…

A: As we know that f=f(x,y,z)then fx(x,y,z)=∂f(x,y,z)∂x, fy(x,y,z)=∂f(x,y,z)∂y, fz(x,y,z)=∂f(x,y,z)∂z