Show that 7(u, v)= (²-²,2ue) maps the triangle-((u, v):05≤SS 3) to the domain D bounded by z = 0, y = 0, and y²-324 36z. Use T to evaluate ₂√² + y dedy Answer:

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Q: $. flx) =3=x*, glx)=x² -4 d) Domain A domain H) Domain

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Q: 5. Given f(x) = x² +4x +2 and g(x) = 2x – 3, find all of the following:

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Q: O Evaluate )ds where c is the line segment from (-2,0) to 0,2).

A: We will parameterize C and solve.

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A: The objective is to find the double integration where  R=[0,1]×[0,2]

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Q: Q1 Find thr relative maximum and minimum of: fx, y) = x² + y² + z?given that 9x? + 4 y² + 2z? = 36…

A: Consider the provided question,  minimize and maximize, fx,y,z=x2+y2+z2                        ....1…

Q: • r : (x, Y, z) = (7, 8, 2) + X(-3, –8, 2) %3D 7 – x y – 8 - x y – 8 2 – z • S : -7 -6 4

A: Given query is to find the angle between two line.

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Q: A) Find all y such that the distance between the points (-1, 5) and (9, y) is 11. y= B) Find ALL x…

A: To find  A) Find all y such that the distance between the points (-1, 5) and (9, y) is 11.   y=   B)…

Q: ジ.キウー。 *り6)e o)。 3-

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Q: If X = U+v , y =U-V then Show that + 2 du? = 2) ( %3D nene Than ded uce that wok cu+ v*+ (u+v) g…

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Q: f () = 10x _75x 179h420 otheline E-(x +h) for what valies f Xis te doneme line of She auale 179x H20…

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Q: TEST FOR HOMOGENEITY: 4. e √x x-2xy x - y

A: A function f(x, y) is said to be homogeneous if f(Kx, Ky) = Knf(x, y)  where n is any real number…

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A: We have the following given ellipse -  xa2 + yb2 = 1   where a<b

Q: The distance between the points P(0, 0,4) and Q(7,6, 8) is V102 Select one: True False

A: According to question,Given points,P0, 0, 4 and Q7, 6, 8

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Q: xy Let z . Then: 4x2 – 5y? | az dz ду

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Q: '5 - i хі+ C) y = 7+ 2i 3 +i,

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Q: Find the distance from the point (-6, −6, 2) to the line Ỉ =(−1,−1,7)+t(4,−8,2),−oo <t<0. <∞.

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