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(1 point) For partial derivatives of a function use the subscript notation, so for the second par...
a. Use the Chain Rule to find the indicated partial derivatives. z = x4 + x2y, x...
a. Use the Chain Rule to find the indicated partial derivatives. z = x4 + x2y, x = s + 2t − u, y = stu2; ∂z ∂s ∂z ∂t ∂z ∂u when s = 1, t = 2, u = 3 b. Use the Chain Rule to find the indicated partial derivatives. w = xy + yz + zx, x = r cos(θ), y = r sin(θ), z = rθ; ∂w ∂r ∂w ∂θ when r = 8, θ = pi/2 c. Use the...
2. Let u(z,t) be a differentiable function on R x [0, 0o). a) Show that the directional derivativ...
2. Let u(z,t) be a differentiable function on R x [0, 0o). a) Show that the directional derivative of u at (x, t) = (zo, to) along v is Dvu(x, t) = ▽u(ro, to) , v b) Solve the following homogeneous linear transport equation ul + uz = 0, u(x,0) =-2 cosx c) Solve the following non-homogeneous equation ut-2uz--2 cos (x-t), u(x, 0) = sin x d) Solve the following second-order homogeneous linear euqation u(z,0) = sin x, ut (z,...
Q4: Fill in the blanks in the following: a. The first order partial derivatives Fulu, v)...
Q4: Fill in the blanks in the following: a. The first order partial derivatives Fulu, v) of the function (F(u, v)= u'sin(u+v+) equal b. The second order partial derivatives Fxx{x,y) of the function (F(x,y) =x’y-In (x²-y)) equal C. The tree diagram of the Chain Rule for the given function w=w(x,y),x=x( P.4.5), y=y(p,u,v), s=s(u,v)pap(t) will be ........... d. The result of Cross Product Dot Product is a... and the result of Dot Product a is a e. The projection of vector...
0 Both first partial derivatives of the function f(x,y) are zero at the given points. Use...
0 Both first partial derivatives of the function f(x,y) are zero at the given points. Use the second-derivative test to determine the nature of foxy) at each of these points. If the second-derivative test is inconclusive, so state f(x,y) - 12x² +24xy – 2y + 72y: (-2. - 2) (6.6) What is the nature of the function at (-2. - 2)? A. fxy) has a relative maximum at (-2,-2) B. fxy) has a relative minimum at(-2.-2) OC. XY) has neither...
Compute the partial derivatives of the function at the given point, and determine what the total...
Compute the partial derivatives of the function at the given point, and determine what the total derivative would be if the function was differentiable there; then determine whether it is differentiable or not by definition; that is, determine whether or not 0. 22+y2 (x,y) # (0,0) fão + n) – $(20) - Df#, (h) lim ho hi 4. h(x, y) = 0 (2,y) = (0,0) at (0,0); 5. g(x, y, z) = x + 3y - 2 - 1 at...
Use the limit definition of partial derivatives to compute the partial derivative of the function f(x,y)...
Use the limit definition of partial derivatives to compute the partial derivative of the function f(x,y) = 2 - 2x + 5y - 3x?y at a point (3.4). a. Find f (3.4). b. Find f (3.4). f|(3.4)=0 (Simplify your answer.) 13(3.4)=0 (Simplify your answer.)
Part 1 of 1 Question 1 of 1 50.0 Points Mark which statements below are true, using the following...
Part 1 of 1 Question 1 of 1 50.0 Points Mark which statements below are true, using the following Consider the diffusion problem, дги ди dx2dt u(x,O)-f(x) where FER is a constant, forcing term Any attempt to solve this using separation of variables fails. This is because the PDE is not homogeneous. A more fruitful approach arises from splitting the solution into the sum of two parts, taking into account that all change eventually dies out. That is there is...
Find all the first and second-partial derivatives for the utility function, U -50x 5y 0.2 (a)...
Find all the first and second-partial derivatives for the utility function, U -50x 5y 0.2 (a) Give a verbal description of each derivative. (b) Are the marginal functions increasing or decreasing. Use the derivatives to justify your answer b. Given the function Q- Al'KB, explain the terms: constant returns to scale; increasing returns to scale; decreasing returns to scale. Show that the production function, Q -100L0.3K0.5, exhibits decreasing returns to scale and diminishing returns to labour Show that the production...
Use the limit definition of partial derivatives to compute the partial derivative of the function f(x,y)...
Use the limit definition of partial derivatives to compute the partial derivative of the function f(x,y) = 6 - 6x + 5y - 3x2y at a point (3,4). a. Find f,(3,4). b. Find f(3,4). 1,(3,4)=0 (Simplify your answer.) 12(3,4)=0 (Simplify your answer.)
Suppose that f is a twice differentiable function and that its second partial derivatives are continuous....
Suppose that f is a twice differentiable function and that its second partial derivatives are continuous. Let h(t) = f(x(t), y(t)) where x = 2e and y = 2t. Suppose that f:(2,0) = 4, fy(2,0) = 3, fx=(2,0) = 2, fyy(2,0) = 3, and fxy(2,0) = 2. Find out that when t=0.
2. Let u(z,t) be a differentiable function on R x [0, 0o). a) Show that the directional derivative of u at (x, t) = (zo, to) along v is Dvu(x, t) = ▽u(ro, to) , v b) Solve the following homogeneous linear transport equation ul + uz = 0, u(x,0) =-2 cosx c) Solve the following non-homogeneous equation ut-2uz--2 cos (x-t), u(x, 0) = sin x d) Solve the following second-order homogeneous linear euqation u(z,0) = sin x, ut (z,...
Q4: Fill in the blanks in the following: a. The first order partial derivatives Fulu, v) of the function (F(u, v)= u'sin(u+v+) equal b. The second order partial derivatives Fxx{x,y) of the function (F(x,y) =x’y-In (x²-y)) equal C. The tree diagram of the Chain Rule for the given function w=w(x,y),x=x( P.4.5), y=y(p,u,v), s=s(u,v)pap(t) will be ........... d. The result of Cross Product Dot Product is a... and the result of Dot Product a is a e. The projection of vector...
0 Both first partial derivatives of the function f(x,y) are zero at the given points. Use the second-derivative test to determine the nature of foxy) at each of these points. If the second-derivative test is inconclusive, so state f(x,y) - 12x² +24xy – 2y + 72y: (-2. - 2) (6.6) What is the nature of the function at (-2. - 2)? A. fxy) has a relative maximum at (-2,-2) B. fxy) has a relative minimum at(-2.-2) OC. XY) has neither...
Compute the partial derivatives of the function at the given point, and determine what the total derivative would be if the function was differentiable there; then determine whether it is differentiable or not by definition; that is, determine whether or not 0. 22+y2 (x,y) # (0,0) fão + n) – $(20) - Df#, (h) lim ho hi 4. h(x, y) = 0 (2,y) = (0,0) at (0,0); 5. g(x, y, z) = x + 3y - 2 - 1 at...
Use the limit definition of partial derivatives to compute the partial derivative of the function f(x,y) = 2 - 2x + 5y - 3x?y at a point (3.4). a. Find f (3.4). b. Find f (3.4). f|(3.4)=0 (Simplify your answer.) 13(3.4)=0 (Simplify your answer.)
Part 1 of 1 Question 1 of 1 50.0 Points Mark which statements below are true, using the following Consider the diffusion problem, дги ди dx2dt u(x,O)-f(x) where FER is a constant, forcing term Any attempt to solve this using separation of variables fails. This is because the PDE is not homogeneous. A more fruitful approach arises from splitting the solution into the sum of two parts, taking into account that all change eventually dies out. That is there is...
Find all the first and second-partial derivatives for the utility function, U -50x 5y 0.2 (a) Give a verbal description of each derivative. (b) Are the marginal functions increasing or decreasing. Use the derivatives to justify your answer b. Given the function Q- Al'KB, explain the terms: constant returns to scale; increasing returns to scale; decreasing returns to scale. Show that the production function, Q -100L0.3K0.5, exhibits decreasing returns to scale and diminishing returns to labour Show that the production...
Use the limit definition of partial derivatives to compute the partial derivative of the function f(x,y) = 6 - 6x + 5y - 3x2y at a point (3,4). a. Find f,(3,4). b. Find f(3,4). 1,(3,4)=0 (Simplify your answer.) 12(3,4)=0 (Simplify your answer.)
Suppose that f is a twice differentiable function and that its second partial derivatives are continuous. Let h(t) = f(x(t), y(t)) where x = 2e and y = 2t. Suppose that f:(2,0) = 4, fy(2,0) = 3, fx=(2,0) = 2, fyy(2,0) = 3, and fxy(2,0) = 2. Find out that when t=0.
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