Give the limits of integration for evaluating the integral || f(r,0,z) dz r dr d0 as an iterated integral over the region that is bounded below by the plane z = 0, on the side by the cylinder r= 6 cos 0, and on top by the R paraboloid z = 7?.

Q: Find the laplace of  f(t) = cos(root2)t + sin (3t)

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Q: 4 sin 3y–6 dy cos 3y

A: We'll evaluate the integral as following.

Q: Use the Chain Rule to find ∂z/∂s and ∂z/∂t. z = tan(u/v), u = 3s + 9t, v = 9s − 3t…

A: The solution is shown in step-2

Q: Let f(x, y) = x sin ry. Find: fyy (x, y) fyz(x, y)

A: f(x,y)=xsinxyfx=sinxy+xycosxyfyx=xcosxy+x(cosxy-xysinxy)=2xcosxy-x2ysinxyfy=x2cosxyfyy=-x3sinxy

Q: Q1J Use the Chain rule to find the derivative of w=xy + In z with re spect to v if x v/u, y u+v, z…

A: The chain rule is used to calculate the derivatives of the function. The chain rule for a function…

Q: ntegrate ze²² dz where C from 1 along the axes to i C

A: (.)   Given integral is,    where  along to the axes to .(.) If a function is analytic then integral…

Q: Find a function f such that Vf = 2e²x cos(5y)i - 5e²x sin(5y)j + z³k. f(x, y, z) =

A: Given :-  = 2e2x.cos(5y)i - 5e2xsin(5y) j + z5kNow,

Q: Express the function f(z) = sin(=) in the form f(z) = U (x, y) + V (x, y)i. %3D

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Q: (0)= I Y+2y-ソ-2y こ 11 (o) =2

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Q: g) The integral S tan(vx) dx x cos2 (Vx)

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

Q: Let r(t) = (cost,sin t, ln(cost)).Find T, N, and B at (1, 0, 0).

A: Let rt=cos t, sin t, lncos t at 1,0,0 Find T, N and B. Tangent vector to the curve is denoted by…

Q: Find fr, fre and fy if: f(x, y, z) = xy + yz + xz %3D

A: We have - f(x,y,z) =xy+yz+xz To Find - fxz, fyz, fxy

Q: a red coin as a 1 on one side and a 3 on the other. a blue coin has a 0 and 1. let X represent the…

A: Given Red coin→ 1,3 Blue coin→ 0,1 X→ Total of both coins Y→ No. flipped on the blue coin

Q: Find a function f such that Vf = 2e²x cos(5y)i - 5e²* sin(5y)j + z5k. f(x, y, z) =

A: The given gradient function

Q: Find f, and f, and evaluate each at the given point. f(x, y) = arctan (2, -2) f,(x, y) = f,(x, V) =…

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Q: find dw/ar if w = (x + y + z)?, y = cos(r + s), at the point (r, s)3(1,-1) x = r - s, z = sin(r + s)

A: Given w=(x+y+z)2 x=r-s y=cos(r+s) z=sin(r+s) point (r, s)=(1, -1)   when we differentiate partially…

Q: Given a function f(x, y, z) = cos (x + xy²z²), find: f#(5,1, 1) = frz (T, 1, 1) = %3D

A:

Q: Solve the sifferential equation using tHce Laplace transforms- you y =I y lo)=y'(0) = y"(0)= 6 %3D

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: Find the gradient of the functions below. a)f (x, y, z) = sin(xyz)

A: Here we will find out the required value.