Explain how the evaluation for each of S. f(x, y) ds, ſ. f(x, y) dx, ſ. f(x,y) dy, and F ( x, y) · d T involves a process similar to trig substitution. Assume that х, C is defined by r(t) = over the interval [a, b].

Q: .3 If U = 2– x, | x 2-xdx=

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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..

Q: (x, y, z) = 2x²y — xz² + 3y²z. Xyx

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Q: If f(x, y): X 2y + 1 use the definition to find af (x, y) ду

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Q: Let X: EXP(0). suppose Y= 2x , the Y is i = 1 Select one: a. Gamma (n,-) b. Camma(n. 4) С.…

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Q: Q (1): Find fxyz for the function: = xe² + ye* + zey a) f(x, y, z) %3D

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

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Q: dz 2 = -ry", where r = st“ and y = –st". Compute – as a function of s and t only evaluate this when…

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Q: 6) Find R100 for y = x³ on the interval [0,2]. Use four decimals.

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Q: 3. Which function has a range of yS 3? Ax) -- +3 с. a.

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Q: = Evaluate S₁2₁,22,23] f (2) dz where 21 = −i, z2 = 2 + 5i, zg 5i and f(x + y) = x² + iy

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Q: Find a such that the distance from (−1, 2) to ax − y + 9 = 0 is √5 units.

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Q: Solve the following initial value problem. y" − 6y' + 5y = 4x + e*, y(0) = 0, y'(0) = 2

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Q: dx. = 9) Evaluate 2x-1

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Q: 2. fote-t² dt

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Q: if r'y-- 2y + 1.

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Q: find the derivative of (2³ + j)² O 23 +j O 223 + j O 625 + j6z² O 325 + j3z?

A: Derivative of (z3+j)2 is 2(z3+j)2-1(3z2+0) = 2(z3+j)×3z2 = 6z2(z3+j) = 6z5+j6z2

Q: Find // VdA, + 1 R -dA, R= [0,3] × [−1,1]

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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: P=S/(S+F) Express S in terms of F and P

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: Q2: Given the function fa) = {(2,1), (,5), (5, lo)) fo, D(f) , R(fw). Find

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

A: Given,