Practice problem 9 Consider F and C below. F(x, y, z) = (y²z + 2xz²)i + 2xyzj + (xy² + 2x²z)k, C: x = √t, y = t + 6, z =t², 0≤t≤1 (a) Find a function f such that F = Vf. f(x, y, z)= (b) Use part (a) to evaluate [F F. dr along the given curve C.

Q: a) Consider the function f (x, y) VIn (4 – x² – y²). Find the domain - and range of f(x, y).

A: Solution is given below..

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A: This is second partial derivative so do the derivative like normal considering all other variable…

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Q: Suppose f(x, y) = xy + 4. Compute the following values: f(x + 4y, x – 4y)= - f(xy, 6x²y³)=

A: We can find the given function .

Q: If f(x,y)=x²y³+x4y, find f XX 2y³ + 12x²y 2xy³+4x³y □ 6x²y 6xy² + 4x ³

A: Topic = Derivative

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A: we have to find the domain for f(x)

Q: (a) Find the domain of V4 – 3w R(w) = w + 2

A: Please complete your question b part its incomplete. What is l ? Here I'm doing (a) part only.

Q: Let f(x, y) = x²y³, then Vf(1,2)= Select one: True False

A: Given problem:- fx,y=x2y3 Then ∇f1,2=16,12?

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A: Introduction: A function is an expression, rule, or law in mathematics that defines a relationship…

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Q: Graph and shade the domain of f(x, y) = vy + x² – 2.

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Q: .Let f, g andh are three functions defined as below : f: R>Rf(x) = 4x² – 4, - g. R→R8 (x) = V-5x+…

A: Given  f(x) = 4x2-4g(x) = -5x+1h(x) = 2x-5   a) fog(x) = f(g(x)) = f(-5x+1) = 4-5x+12-4 =…

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Q: z) = (x2 + then (a + E

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Q: 2. Sketch the domain of the following functions: a) f(x, y) = b) f(x, y, z)= 2-x-y - eª %2 In(4-x² -…

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Q: Q1: If w-f(z)=z'-z²+2z+2 find u and y and calculate the value of f at z-1-21. V.

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Q: Select the option that gives a list of the stationary points of the function f(x, y) = x³ – 3x² –…

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Q: 3. Find V x F for F(x, y, z)= -x2 i + x² + y² -yz x² + y² =j+√x² + y²k.

A: Given function:To find Known facts:

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Q: Let Find fa, fay and fryz f(x, y) =In(xy)-26x¹0 y 10

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Q: The domain of the function f (x, y) = In(2 – /x² + y² ) is:

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Q: |(0,3) C1:x2 + y? = 9. (-3,0) C2 (3,0) Figure 1 Based on Figure 1 and given that F = y²i + (3xy +…

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Q: 3) Show that f = f, ху for the following function: ху (x° у) f(x. y) + In(x° + y30 ) 20

A: We have to prove that fxy = fyx

Q: 2. In each case, write the function f(z) in the form f(z) = u(x, y) + iv(x, y): z² (a) f(z)=z³+z+1;…

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Q: Compute fx, fy and fz for the function and evaluate them at the indicated points

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Q: 1. Identify and sketch the domain of f(x, y) = √y² + 4x + 2 In(1-x² - y²)

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Q: Suppose f(x, y) = xe -8x²-8y². Answer the following. 1. Find the local maxima of f. List your…

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Q: For the function f(x,y) = 3 x³ + 5y4 5 4 x +y find f, fy, f(-1,1), and f,(-3,2).

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