I Suppose that f(x, y) = at which {(x, y) | 3 ≤ x ≤ 5,2 ≤ y ≤5}. y D Then the double integral of f(x, y) over Dis S [ f(x, y)dady = where In(x) can be input by "In(x)".

Q: Show that the line integral | 2.xe- dx + (2y – a²e¬") dy is independent of path and evaluate the…

A: Here we have to show that the given line integral is path independent and evaluate the line integral…

Q: 9) Evaluate the double integral of the function f(x, y) = 12x²y + 8x³ over the rectangle 0≤x≤ 2 and…

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Q: 4. Let f(x, y)=2x*y' . Find f,(x,y)

A:

Q: Show that f = {(x, y) ∈ R × R; x = y^3} is a function from R to R

A: Given, The function f={(x,y)∈R×R ; x=y3 }   We have to show that the given function is from R to R.

Q: What is the integral of the constant function f(x, y) = 5 over the rectangle [-2, 3] x [2, 4]?

A: Given:            f(x, y) = 5   over rectangle -2, 3×2, 4

Q: Given F = < x^2y, x > and c is the line from P1 (2,1) to P2 (0,0) Find the integral of F • dr

A: Firstly, we find the equation of line joining (2,1) and (0,0) by using two-point form of equation of…

Q: Let F(x , y , z) = g(y) + h(z) + 5 In(x - 2) , where g(y) and h(z) are differentiable functions of…

A: If a function is a function of more than one independent variable then the derivative of this…

Q: Is the function f(x) = ( 1, x not equal 1)             ( 0, x equal 1) integrable over the interval…

A: Here, we will show that the given function is integrable. Let us take a point c ∈ (0,1).

Q: Let F = 10xe³i+ 5x²e³ j and Ğ = 10(x − y)i + 5(x + y) j. Let C' be the path consisting of lines from…

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Q: Assume that f: R→ R and g: R → R are infinitely differentiable functions. Prove the following…

A: We have given that ,  are both infinitely differentiable.We need to prove that , We will use…

Q: Integrate the function ƒ(x, y) = 1/(1 - x2 - y2) over the disk x2 + y2<=3/4. Does the integral of…

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Q: For f(x, y) = xe**Y, find fy (1, In 2) O 2 O 2 In 2 O 4 In 2 +2

A:

Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

A:

Q: II. Let f(x, y, z) = z° sin a + Determine 2 dydzərəz'

A: We know, ∂2f∂y∂x=∂∂y∂f∂x

Q: Evaluate the integral S (tan - dy ¹(y/3)) (9+ y²)

A: This is Indefinite integral because no limit

Q: Evaluate the integral S (tan(y/10)) (100+ y²) dy tan ¹(y/10)) (100+ y²) dy 11

A:

Q: Suppose f is differentiable at (3, 4), V f(3, 4) = (-V3, 1), /V3 and u = Compute D„f(3, 4). 2

A: ∇f3, 4=-3, 1, u=32, -12

Q: alculate D(f ◦ g) for the fun

A: answer is in next step

Q: Let F(x, y, z) = (6x5 ln(5y² + 3) + 3z7)i + (· +6z)j + (21xz6 + 6y − 3ä sin íz) k 10yx6 + and let…

A: