Suppose that f(x, y) D [ f(x, y) dx dy X = - and the region D = [2,3] x [2,5]. Y =

Q: vinarixinvaxana Pic г.) 4. Find Brune fronor. [

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Q: Let f (x, y) = 2x3 + x2y - y2. Compute d2f/dx2, d2f/dy2, and d2f/dxdy at (x, y) = (1, 2).

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Q: Suppose f(x, y, z)=x+y+z, h(x,y) = (x + y, x³, y) and g(x) = (x,x²). Calculate d =z=of oho g(x). dx

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Q: Indicate whether the following statement is true or false. Let f(x, y) be any c' real valued…

A: Given fx,y be the C1 real valued function defined on the rectangle R=a,b×c,d. Then we have to check…

Q: Find [2² Pex. 2 √²+ 3 1³ F(x f(x, y) = 5x + 3x²y² 3 √³ F(x, f(x, y) dx and f(x, y) dx = f(x, y) dy =…

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Q: Let f= 2zy + yx, v= [y, z, 4z -x]. Find Dyf at (2,1,2). NOTE: Enter an exact answer. Dvf (2, 1, 2) =

A: Given: fx, y, z=2zy+yx, v=y, z, 4z-xTo find: The directional derivative, Dvf at 2, 1, 2

Q: Find y in terms of x. dy = x 2 + 5, curve passes through (0, 14) dx x3 A) y = + 5x 3 B y = x3 + 5x +…

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Q: Find an absolute extrema of f(x,y)=2x² - 4x + y² - 4y +1 on the closed triangular region bounded by…

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

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Q: Suppose that f(x, y) = 7, and D = {(x, y) | x² + y² ≤ 1}. S f(x,y) dx dy =

A: Tou have to know the following result to solve this problem

Q: Evaluate SSS 5el=²+g²+z?)*² dV over B where B = {(r, Y, z) : z² + y² + z² < 1}. Take 7 = 3. %3D

A: A triple integral involves the integral with respect to the product of the variables x,y, and z. In…

Q: Evaluate (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (7,-5)

A: The given integral is ∫C2x-y dx+x+5y dy where C is the line from 0,0 to  0,-5 and  0,-5 to 7,-5. To…

Q: 5-find for y= (r² + 1)1 ,x (4r + 1)2 (use chain nule) %3D dx A)y Vr+1 (r2+1) dx dy r(4r + 1) B) dx…

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Q: where Dx = X₁-X₂ and Dy = |Y₁ — Y2]. Assume that the two locations are independent and uniformly…

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Q: Where did F(x, y, z) = Em(1,4,5) come from

A: The steps to follow to write a function in SOP form:    1. Write AND terms for each input…

Q: 2. Evaluate dx + (-xy + x²) dy along C: y² = x from (0,0) to (1,1).

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Q: 14. We know that S(x,y)dx+g(x,y)dy] = Se f(x,y)dx + Se g(x, y)dy. Use this knowledge to evaluate S.y…

A: We integrate this by making two path where for one path only y vary and for other path only x vary.

Q: Let F(x, y, z) y³ 2:5 . What is the value of div F at (1, 2, 3)?

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Q: 2. Find Df(x, y, z) for f(r, y, z) =x In z+r+ y at (0,0, 2).

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Q: dy : Find if dx 3.x 2) x - y 4+ y x +y 4) xy² x - y

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Q: Let f(x, y) = x³ + y³ + 3x²y + xy + y². Find fæ, fy, fax, fry, fyy.

A: The given function is,

Q: If y (x, t) is a function of x and t, prove that i) Lat =py (x, p)- y (x, 0) ii) L- = p°y (x, p) –…

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Q: Let f(x, y) = xe Ty", find fr, fy, fræ, fay and fyy-

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Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

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Q: Let f(x, y, z) = x2 (e)^y/z. Compute f(-1, 0, 1), f(1, 3, 3), andf(5, -2, 2).

A: Let fx,y,z=x2eyz 1. we have to compute f(-1,0,1) as, fx,y,z=x2eyzHere x=-1, y=0,z=1f-1,0,1=-12e01=1…

Q: 3. Find all functions from X = {a,b} to Y = {p,r, t}.

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