f(x,y,z)=x²+yz² 1) find gradient of  f )find integration on c to gradient of f

Q: Calculate the double integral. 6x/1+xy dA, R=[0,6]x[0,1]

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Q: 8. The region of integration D is bounded by the lines y = x,x + y ==,y = 0. Show that 1 | sin(x +…

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Q: Evaluate triple integration of xz *dv with respect to E where E is the solid tetrahedron with…

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Q: )Find volume of body from above Z = 1- y² and below 2 = x² using Triple integration.

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Q: Find a potential function for F. f(x,y,z) =

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Q: 2. Given that f(t) = f cos x cos(t − x) dx, fin integral.

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Q: Find the moment of inertia with respect to y-axis the area bounded by x2- 4y + 8 = 0, the lines x =…

A: The given question can be solved as shown in step 2.

Q: The region bounded by y = v9– x² and y = 0 has an area of . Find the y-coordinate of its centroid.

A: Suppose the region is bounded by fx and gx on a,b where fx≥gx .Assume centroid is denoted by x¯,y¯…

Q: Find i Pontial dlexivalive Sur face level Ü) Li) F Gradient of iy Tongen planes 4 funct ion Z= Cos…

A: (i) Given the function is z=cos-1x+y. Find the partial derivatives.…

Q: 4-x? Change the order of integration | | f(x, y, z)dzdydx in the order dydxdz.

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Q: dz 4z+z' ,2

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Q: The area bounded by y=1-x² and x+y=1 is submerged vertically in the water with the water level in…

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Q: Plot a direction field and some integral curves for xy' - 2y = -1 (A) on the rectangular region {-1…

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Q: Sketch the region R of integration and switch the order of integration. 49 f(x, y) dy dx 50 3 40-…

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Q: Find the line integral of F(x, y, z) = x³i + yj+ zk along th the origin to the point (3, 2, 6). F.…

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Q: Find the total differential of W = x^4 y^3 z^2 + x^3 Y^2 + x^2 z +y + 3 at (2,1,1)

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Q: Sketch the region of integration. (x, y) dx dy y y (0, 9) |(9,9) (0, 9) (9, 9) y=x y=x

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Q: . The solid bounded by z = 1 – x², z = 5 – 2x², y = 0, and y – z = 6. |

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Q: Find the moment of inertia with respect to y-axis the area bounded by x2- 4y + 8 = 0, the lines x =…

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Q: a" cos xdx

A: the given integral is: we have to evaluate the given integral

Q: Find the moment of inertia of the solid formed by revolving about ox the area bounded by a^2y=x^3,…

A: The given problem is to find the moment of inertia of the solid formed by revolving about an x-axis…

Q: Find the linear approximation to f(x, y, z) = at the point (2, –1, –2): f(r, y, z) z

A: A Givenfx,y,z=xyz at the point 2,-1,-2linear approximation at the point…

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=0,…

A: I am going to solve the given problem by uisng some simple calculus to get the required result.

Q: Find the gradient of f(x, y, z) =e^y cos(xz) at (1,0,1) .

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Q: Find the moment inertia of the solid formed by revolving about ox the area bounded by a2y=x3, the…

A: Solve the problem

Q: What do we get when we reverse the order of integration in the double integral (z, 4) dy dz? •y/2 I…

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Q: 2) Show that the integral f. (cosyz dx – xz sinyz dy - xy sinyz dz) is path independent and find its…

A: Condition for line integral to be path independent is given below. ∫cFdr is path independent if F…

Q: The amount of work that a force field does on a particle as it moves along the boundary of a…

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Q: line integral x³ dy), where y is t 3 X counter clockwise.

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Q: 3. ) Compute for the increment of the function f(x,y) = *+3y . Also, find the total differential of…

A: w = f (x, y) and let ∆x and ∆y be increments of x and y respectively. The increment ∆w of w = f (x,…

Q: Write the approximate change formula for a function z = ƒ(x, y) at the point (x, y) in terms of…

A: Consider the following function: z=fx,y

Q: Find the potential function for F(x,y,z) = (x^-1z)i + (y^-1z)j + ln(xy)k. Show all steps and explain

A: Potential function of  F, is f such that ∇f=F.

Q: VT VT "cos(x?)dxdy? What is the reversed order of integration of "y O a. cVT X cos(x²)aydx 0. O b. V…

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Q: Find the moment of inertia with respect to y-axis the area bounded by a²y = x³ , the x-axis, and the…

A: Given....

Q: Evaluate the line integral $ x*dx + xydx where C is the triangle with vertices at (0, 0), (0, 6) and…

A: Given Line Integral is ∮x4dx+xydy , where C is a triangle with vertices at (0,0), (0,6) and (6,0)…

Q: Find the total differential of z= f(x, y), where f(x, y) = In Use * for multiplication of variables,…

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Q: Find the moment of inertia with respect to the y-axis for a flat plate covering the region bounded…

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Q: Find the linearization of f (x, y, z) = xy / z centered at (2, 1, 2). Use itto estimate f(2.05, 0.9,…

A: Our Aim is to find the linearization of f(x,y,z) =xyz centred at (2,1,2).and then using that value…

Q: Vy+I ydx dy -1 -Vy+1

A: Let's find.

Q: Integrate f(x,y,z) = x-3y + z over the line segment joining the points (0,0,0) and (2,2,2). %3D

A: Here, we need to integrate f(x, y, z)=x-3y2+z over the line segment joining the points (0, 0, 0) to…

Q: 6: Change the order of integration; -1 f(r, y)dydr + f(r, y)dydx

A: Interchange the x and y limits For first part y=x⇒x=y2x=0, y=0x=1, y=1∫01∫0x f(x,y)dydx=∫01∫0y2…

Q: compute the line integral of the function f(x,y,z) = x^2 +3y along the circle x^2 +y^2=4 from (0,0)…

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Q: Which order of integration is preferable to integrate ƒ(x, y) = xyover R = {(x, y): y - 1 ≤ x ≤ 1 -…

A: Given: fx,y=xyR=x,y:y-1≤x≤1-y, 0≤y≤1 To Determine: Which order of integration is Preferable to…

Q: Use the Chain Rule to find dQ where Q=√√3x² + 3y² + 4z², x= sint, y = cost, and z= cost. dt'

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Q: A lamina is bounded by y-e and the lines y-0,r-0, and zI with density (r,y) - y. Find the moment of…

A: Calculate moment of inertia about y-axis:

Q: Let p(x,y) = e2*y+4y and let F be the gradient of y. Find the circulation of F around the circle of…

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Q: Find the total differential of w ze(z+y) at (0,0, 1).

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