Let f(x, y) = x² – xy + y? – y. Find the directions u and the values of Duf(1, –1) for which %3D Duf(1, –1) = 0

Q: If f(x, y) = 4e*y cos (x- 1) , then the linear approximation at (1,0) is | (A) 4 + 16x (B) 4 + 4x…

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Q: Given f(x, y, z) = 3x – 2y + 1z, find f. (æ, y, z) = fy(x, y, z) = f:(x, y, z) = |

A: We are given with the function f(x,y,z) and need to find the derivative fx,fy and fz.

Q: Let f (x, y) = 3x2 + 2xy + 5y. (a) Calculate df/dx (1, 4). (b) Evaluate df/dy at (x, y) = (1, 4).

A: Differentiate the function f with respect to x treating y as a constant to calculate ∂f∂x.

Q: Given z = f(x – y, 2x – 2y, 3x – 3y). Show that dz dz + 0. ду

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Calculate dw/du and dwldv using the following functions: = f(x, y, z) = 3x² – 2ry + 4z2 = x(u, v) =…

A: Apply chain rule

Q: Given: y = f(u) and u = g(x), find dy/dx: %3D a) у %3D сos u, и%3D—х/3 -x/3 u = b) y = tan u, и 3D…

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Q: Let y = x2 – 4.x. With x = 5 and Ax = 1, find the values of Ay and dy. %3D %3D -

A: y=x2-4x , x=5 and ∆x=1

Q: Find dw/dt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

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Q: Find the linearization L(x, y) of the function f(x, y) at P0 Then find an upper bound for the…

A: We need to determine the linearization of the function: f(x, y)=xy2+ycosx-1 at P01, 2 over R:…

Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y 2- ax ду dv

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Q: C is given by x = t°, y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + x dy + y dz)

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Q: Q.1B) If w = f(u, v) where u = tan-12 & v = In(x² + y²),the show that: %3D dw aw aw +y- = 2 ax ду dv

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Q: Solve the following function by applying the chain rule. w = xyz x = u?v y = uv? Z = u? + v? %3D…

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Q: Obtain ∫C  ez / (z - πi) dz with C defined as z(t) = 4eit and 0 ≤ t ≤ 2π

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Q: Find the solution u(x, y) of u+sin(r) uy = y for z, y ER, u(x = 0, y) = 0.

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Q: Ut for 0 <x <l u(x,0) = x u(0, t) = (1, t) = 0

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Q: f({x, y))) for all c e R and all (x, y) E R?

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Q: Given the function: f(x,y) = x cos (xy) – x²e*Y - Find fa(x, y) а. b. fy(x, y) a fzy(T, y) C.

A: As per our guideline we are supposed to answer 3 sub parts of a question please repost the other…

Q: H.W: Find fr, fyand f if f(x,y, z) = x-Vy +z

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Q: Let f(x, y, z) = x² + 2y+ e³=2« + 2°. Find the rate at which f is changing at (1,2, –1) in the…

A: Use the formula of the directional derivative and simplify.

Q: Given f(x,y,z) = x³yz². Find fy(1,1,1)

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Q: Find dw/dt using the appropriate Chain Rule. w = x? + y? x = 3t, y = 10t dw dt

A: We have to solve

Q: K is between J and L, KJ= 46, and KL = 47. Find JL. Y f(X) Vx X,

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Q: Given z = f(x – y, 2x – 2y, 3x – 3y). Show that dz dz 0. dx fie +

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Q: Find - given that dt dx x? + y? = 2x + 4y, x = 3 y = 1, and dt 11 dy i dt II

A: Given problem is :

Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y¬ 2- ax ду…

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Q: Find aw/@s and dw/at using the appropriate Chain Rule. Function Values .3 W =V 4, t = 8 X = e, y = e…

A: We can solve this as follows:

Q: (e) Find and classify the stationary points of f(x, y) = x³ – 6xy + 8y³. %3D

A: Solution   c f(x,y)=x3-6xy+8y3       first we write down the partial derivative of f(x,y)…

Q: 2. For what value(s) of h, y belongs to Span {v1, v2, v3}? Where 5 -3 V2 = -4 V3 ,and y = 3 h

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Q: Given f(z, y) = 7x° cos (y*), find fzy(z, y) = | fyy(T, y) = [

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Q: For f(x, y) = e3r +y, find Preview a. fr b. Jy Preview Preview c. f„(1, 1) = Preview d. f,(1, 1) =

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Q: Find the linear approximation of y = V1+ x at x = 0 and use it to approximate V1.05 7.

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Q: f(x, y) = e&z– 4y af af ду

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Q: dz and Use the chain rule to find du for z = 4x?y3 – 2x² + 3y where x = uv and y = u –- v

A: Given, z=4x2y3-2x2+3ywherex=uv and y=u-v

Q: If z = f(x, y), where x = 2ts and y = t2 + s², show that () - 2 + 2x + 4y %3D dsdt

A: Here given z=fx, y and x=2st, y=s2+t2

Q: Let y = f(x1, x2, w), where x1 = 2w2 and x2 = w+1. Find dy/dw.

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Q: Let f (x, y, z) = xy + z. Calculate - df/ds, where as x=s2 , y=st, z=t2

A: Given f(x,y,z) =xy+z , x=s2 , y=st and z=t2. We need to calculate -df/ds.

Q: Find vf(x, y) if f(x,y) = e* c cos y 5.

A: Note : according to our guidelines we can answer only first question because there are multiple…

Q: Given f(x, y, z) = x³yz². Find fy(1,1, 1).

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Q: The function f(x,y) is homogeneous of degree one. cos a) True b) False.

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Q: Is F(x,y)= (2²y,5– zy²) source free?

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Q: Given y = f(u) and u = g(x), find dy/dx = f'(g(x))g'(x). %3D %3D y = u?, u = 2x - 4 %3D %3D

A: Given y=u2,u=2x-4 y=f(u) and u=g(x) dy/dx =f'(g(x))g'(x)

Q: Find f, for f(x, y) = | cos(r*) dt.

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Q: Let z = f(x, y) = In(x² + y²), when x = 2, y = 3, and dx = 1, dy = 0.5, then %3D %3D %3D dz = Select…

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Q: Suppose A = xy" where x, y e R". Show that ||A||2 = ||x||2||y||2-.

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Q: Let f(x, y, z) = 3x?y+ yz3, where x = 3 – t2, y = 2t + t3, and z = V1+ 3t. Calculate when t = 1.

A: NOTE: Refresh your page if you can't see any equations. . here we have . the given function is…

Q: An integrating factor (of the form u(x, y) = x" + y") for the DE. ydx + 5xdy = 0 is O is + y * + y?…

A: Solution: The objective is to find the integrating factor of the given differential equation

Q: Find Vf(x, y) if f(x,y) = e** cos y ..... ...

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Q: Assume that w=f(s° +t) dw dw and ds and f'(x) = ex. Find - dw %3D at dw ds

A: Given : w=f(s3+t2)  and f'(x)=ex