H.W: Select the divergence of F(x, y) i+ (2x – 3y)j. %3D 1 (b) -* +2, y2 1 (c) (a) 3, (d) -2. - - -

Q: Use e – 6 definition and show that the function 4x² – y? if (r, y) # (1, –2) 2r + y f (r, y) = • 4,…

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Q: Consider the function P(x) = (x – 2)°(x – 6) - The y-intercept is the point (0,-24) The…

A: Recall: The x intercept is the point where the line crosses the x axis .At this point y=0. The y…

Q: 3. Find the largest domain (in R2) for the function In(3 + y) 1- x + y f (x, y) :

A: Let's find.

Q: Suppose that f(æ, y) = e" = e-3z? - 4y? +y

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Q: b) Find the slope of the function f(x) = VI+1at point (15,4).

A: The slope of  f(x) at a point (a,b) or x=a and f(a)=b is given by, df(x)dxx=a or f'(a)

Q: (x, y, z) = 2x²y — xz² + 3y²z. Xyx

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Q: Tgir.y) = (2ry, 1+2+) and g(1.0)=8, then g(4.1)-9(2.1) =

A: Topic:- calculus

Q: Derivative of y = 16 is: a) 1 b) 0 Derivative of f(x) = - 6x + 2 is: a) - 4 b) 2 Derivative of g(x)…

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Q: of and ду of For the function f(x,y) = In (x+ 3y), find

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Q: 3. (b) Consider the function f(x, y) = a(x² + y²) + xy + 1 for some real number a. Find Vf. Find fxx…

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Q: √x² + y² x-1 (a) Find and sketch the domain of f (x, y). 2. Consider the function f (x, y) = 4 (b)…

A: The given function is  f(x,y)= x2 +y2-4x-1 We know that the domain of a function is the set of…

Q: Find and sketch the domain of z = f(x, y) = In(9 - x - y²).

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Q: The function f(x) = 6e-2x is concave upward over the interval: a b C Od (1, +∞0) (-∞, +∞0) (-∞0, 0)…

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Q: Transform the following point, using the given rule: (-3,8) Rule: (x,y)-> (x-8, y+2)

A: A coordinate system is a convention that is used to represent a point uniquely using a set of…

Q: Find all local extrema of the function f given by f : R? → R, f(x1, r2) = 3x7x2+ x} – 3a? – 3x3 + 2.

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

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Q: дz x² + y², x = 2x + 3t and y = s + t. Find and in two ways: Ət Let z = x дz əs (a) By Chain Rule.…

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Q: Q1. Let X = {m,n, p, q}, {ø, X, {p}, {m,n}, {p, q}, {m, n, p}, {q}} and Y = {a, b, c}, F =…

A: A function is continuous if preimage of every open set is open A function is open if image of every…

Q: Fast please..

A: Let's delve into the explanation of each part of the problem:### Part (a) Explanation:####…

Q: Sketch the domain of f(x, y) = √4x² - y² x - y² on the ry-plane.

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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: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

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Q: Q1. Let f: N x N R be defined by (a + 1)(a + 2b) f(a, b) – 2 Show that the image of f is contained…

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Q: do f() dr where f() = - sin o + sin o cos o = sin ø(y cos o- 1).

A: Given dϕdr=fϕwhere fϕ=-sinϕ+γsinϕcosϕ=sinϕγcosϕ-1

Q: Consider the function y -62 Which of the following statements is true for y? = ze Oy" = 36y…

A: Given,