Use Stokes's Theorem to evaluate F. dr. In this case, C is oriented counterclockwise as viewed from above. F(x, y, 2) = z²i + 2xj + y²k S: 7 = 1- x2 - v2. z >0

Q: a) f : R? → R, f (x, y) = Vy sin x 5) f : R2 → R. f (r. u) = GGrul + In (a2 + 1? – 1). /4 – 72 -

A: We will find the domain

Q: Which of the following is the directional derivative of f(z, y) = at the point (0,0) in the…

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Q: Find the gradient of f at the indicated point. f(x, y) = sin x² + cos 3y; (V.0) NOTE: Give your…

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Q: Find the Jacobian ∂(x, y) ∂(u, v)for the indicated change of variables. x = 3uv,  y = 2(u − v)

A: on solving this we get the

Q: Find the linearization of f(x, y) = V1+x - y? at (4, 1), and then use it o approximate f(3.96,…

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Q: Consider the differentiable function f (x, y) = x2+ y2. Find an equation for a plane that •is…

A: Solution:  Consider the differentiable function f (x, y) = x2+ y2. Find an equation for a plane that…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS PLS

A: Ans 1: (d) Degree of polynomial is 6Ans 2 : (b) Function changes its sign at x =…

Q: O Using part (a), compute the directional derivative of f in the following case: 12 3 4 f(x, y, z) =…

A: I am solving  only part (b) as you mentioned.

Q: The set of functions {Vx, x, x²} is linearly dependent on (0, oo). True False

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Q: 1. Consider the matrices A₁ 4 = ( 1 ) - 1 3 0 A₂ 42 = (3-2) ₁ 4₁ = ( 2² -2²), , A3 0 -2 These…

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Q: For f(x,y, z) = x² – (1 – y)² + z?. Find directional derivative of f at P(1,1,1) in the direction of…

A: The directional derivative of a function f  in the direction of the vector u is given by…

Q: Show that the function given by f(x,y)= x² + 3xy is differentiable at every poin using the…

A: Introduction: Distinctiveness (differentiability) implies continuity. If a function is…

Q: Let f (x, y, z) = xyz. Determine the value of fryy + fyay – 2 fyyr Simplify your answers.

A: We have to find the value.

Q: post office sells 4-cent sheep stamps and 2-cent sunset stamps. Cole bought 5 stamps spent exactly…

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Q: 1(x, y, z) = ln(2x + 4y + z²), at the point u = (−1,1,0), in the direction of the unit vector…

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Q: Let F be the fluid force on a side of a semicircular plate of radius r meters, submerged vertically…

A: Given: Radius of the submerged plate is r. (a) The figure below represents a schematic diagram.…

Q: Find the final amount of money in an account if $8,100 is deposited at 6.5% interest compounded…

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Q: (- 4,3). a) Let f(x, y)= x²y°. Find the directional derivative of f at P(-1,1) in the direction of ū…

A: a)

Q: frxy, 2) =x*j+ x2 +xyZ direction of ū - (1,2,3) 10 5 in the

A: solution of the given problem is below...

Q: (B): use the directional derivative to estimate how much f(x, y) = cos(xy) + xy² Will change if the…

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Q: Consider the equation x25 + y3 + z4 + sin(xy − z) = z2. Find ∂z∂x at the point(1, 2, 2)

A: The objective of the question is to find the partial derivative of z with respect to x, denoted as…