b) Use the divergence theorem to compute f. F ·ñ dS, where S is bounded by x + y + 2z = 2 located in the first octant and F = (2x² – y²,4xz – 2y, xy³).

Q: Let F(t) = (- t + 1, t – 2t", - 2t). Find the line (L) tangent to r (t) at the point (- 15, – 24, –…

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Q: Find (url and dive rgence the of F(xy2)=Xy2 i+ 2x Y j t z(os xyk.

A: Given: F(x, y, z) = xyz i + 2xy j + 2cosxy k To find: Curl and divergence of the given function.

Q: Q2) homeomorphism. Prove or disprove: The function f: (R, T1) - (R, 13) defined by f(x) = 3x is a…

A: Clearly the given function f(x)=3x is continuous. Now we want to check whether it is bijective,

Q: Find the adjoint of F:C3 tends to C3 defined by F(z1, z2, z3)=(2z1+(1-i)z2 , (3+2i)z1 -4iz3 ,…

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Q: - Integrate the function f orgy) =y-Vx over triangle cut from the first quadrant by Line X+y=1

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Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

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Q: 4. a) Find an approximation for f (x, y) = at the point (1.97,1.02). V10-r-5y b) Check Euler's…

A: (a) Approximate f(x,y)=410-x2-5y2 at the point (1.97,1.02) (b) Check Euler Theorem for…

Q: Let C be the counterclockwise boundary of the region enclosed by the x-axis, the line y = x – 2, and…

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Q: If f (s Continuous then on -fex) True or felse?

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Q: prove that t1 = T2 is a necessary and sufficient condition for the unit function Id: (X, t1) → (X,…

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Q: b) Use the divergence theorem to compute ff, F ñ ds, where S is bounded by x+ y + 2z = 2 located in…

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Q: 5. Calculate the divergence of F = (7x², 9y, -52).

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Q: ) Verify the continuity of the function f(x, y) 26– 2x -- y at the point (2,-3).

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Q: Let 7(t) = (- 5t + 2, t² – 4t³, 3tª). Find the line (L) tangent to 7(t) at the point (7, 5, 3) L:(x,…

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Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: If F(t) = 2xyi + xyz2j + ex+yk, then what is the divergence of F? Select one: A. 2yi + xz2j + ex+yk…

A: The divergence of a vector F=P,Q,R is given by div F=∂P∂x+∂Q∂y+∂R∂z. The given vector is Ft=2xy…

Q: |. consider the function f defined by f(x) x€ (-1,1). 3 Vin Cl+z)-Sec (x) a) Find linearteation of f…

A: Definition: Let f(x) be differentiable function on the given domain. The linearization L(x) of f(x)…

Q: Find the divergence of F(x, y, 2) = x²zi + xy²j + (v² + 2)k. Select the correct answer below: O 2xz…

A: Use the method of divergence to solve this problem.

Q: Find fy if f(x, y, z)=1-2xy²z+x²y yxy B) -4z O A) 4z O C) -4 O

A: Sol

Q: Determine the set of (x,y) E R² for which the function f(x, y) = 3x² + [y] is differentiable by…

A: Solution: f(x, y) = 3x2 + |y| => f(x, y) = 3x2 + y if y ≥ 0                     3x2 - y if y <…

Q: b) Compute f. F. dr where c is the boundary of the square [0, 1] × [0, 1] where F = (–y², x²).

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Q: Let S be the sphere of radius 2, oriented inward. Let F = (2x + e", 4y + e*, 2:2). Use the…

A: In the given question we have to solve the double integral s.t∫∫F.ds  to the help of divergence…

Q: Let F = (2xz+y², 2xy, x²+1), if Vf= F, find f(1, 1, 1) – f(0, 0, 0)

A: Given vector funtion and

Q: Consider the function f: N× N → Q given by f(x, y) = your claim. X y + 1 Find the image of f and…

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Q: Study the continuity of f(x,y) = xe-Vx at p(1,0) ey.

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Q: P be the tangent plane to the graph of g(x, y) = 16 - 8x² - 16y² at the point (4,2,-176). Let f(x,…

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