Find the average value of f(x, y) over the region R. f(x, y) = ex + y R: triangle with vertices (0, 0), (0, 9), (9, 9)

Q: Evaluate f(x, y, z) dV for the function f(x, y, z) = xz² and region B = [0, 3] × [5, 7] × [4, 5].

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Q: Express dw and ds interms of rand s, where w = x2 + y?x = r – and y = r +.s = 5rand w as = 38 4rsand…

A: topic - derivatives note : As per bartleby guidelines, we are supposed to answer only first question…

Q: Here is the contour plot of a differentiable function f. 2- (a) Evaluate f(2, 1). (b) Estimate fa(2,…

A: (a) Since the contour line which passes through point 2, 1 has a corresponding value 3. Therefore,…

Q: (3,8, 0) is u x v = %3D So the cross product of u = (1, 0, 1) and v =

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Q: Find (x, y, z). (Let P = (7, 7, 0) and the Midpoint = (0, 5, 5).) (х, у, 2) %3 Midpoint (х, у, 2) P

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Q: Find the absolute maximum and absolute minimum values of the function f(x, y) 2x3 + 3xy + 2y %3D…

A: We have to find the absolute maximum and absolute minimum values of the function fx,y=2x3+3xy+2y3…

Q: 2. Find normal line to zero level surface of: f(x,y, z) = exy, Po(2,5) %3D

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Q: Find the symmetric equations for the normal line LN to the surface S:f (x, y) = 5Vx2 + y? at the…

A: if  f is  function of (x,y,z) then gradient of f is defined asfx i + fy j + fz k ∇f is the normal to…

Q: f(y) = 3{/v +Vv- 2V a. f'(V) = 12y O b. 9Ny-6Vy-8/y 12y Oc. 9y +6Vy- 8v 12y O d. 9+6Vy +8Vy 12y

A: Topic:- Derivative  correct option = c

Q: If S(C) = {; ; Osts1 then from the definition of the Laplace transform t>1 1-e-s Show that L[f(t)]…

A: Solution:

Q: Find the maximum value of f(x, y) = 11zy(9 – 99x – 9y) over the triangle with vertices (0, 0). (†,0)…

A: Given: The triangle vertices are (0,0),(111,0) and (0,1) f(x,y)=11xy(9-99x-9y)…

Q: Q2 Let C be the line segment joining the origin and the point (2,0, 1) and C2 be the line segment…

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Q: Describe the domain of: Зху 3) f(x, y,z) = 4) f(x, y,z) = 1-x² – y² – z2 z- VX

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Q: Find Vf (Gradiant f) for f(x,y, z) = ysinx + yz at p(0,1,2) Please choose one: a.(1, -1.2)…

A: The gradient of a function: f(x, y, z) is defined as: ∇f=∂f∂x,∂f∂y,∂f∂z, where ∂f∂x,∂f∂y,∂f∂z are…

Q: Find fy, fy, and f,, and evaluate each at the given point. X' Z' f(x, y, z) = xy + 2xyz – 8yz, (-3,…

A: Using partial differential equation, we can find required results

Q: Calculate the first time the solution of ty(4-y) 1+t reaches y = 3.99 and determine lim,→∞ y(t). d…

A: Given Data: Let us consider the given data, ddtyt=ty4-y1+t; y0=2 To Find: limt→∞ yt

Q: of Let f(x,y) = xy° +7. Evaluate at (x,y) = (-7,1) and interpret the results. ду -

A: In this question we have find δfδy at (x, y)=(-7, 1)

Q: Determine whether T is linear , if not state whether it is the additivity or the homogenity property…

A: Determine whether T is linear , if not state whether it is the additivity or the homogenity…

Q: . Let u = [1, 7, 4]), v = [1,5, 5), and w [35, 25, 20]. Find the critical point of f(x, y) = (x · u…

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Q: Select all lines that are parallel to the plane x+y+z%= 3. OF(t) = (1,1, 1) + t(1, 1, –2) OF(t) =…

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Q: W(s, t) = F(u(s, t), v(s, t)), where F. u. and v are differentiable. If u (6,-6)= -2, u,(6, −6) = 3,…

A: The objective of the question is to find the partial derivatives of W with respect to s and t,…