2.r + y Find lim (x,y)→(0,0) 2.x²y + xy² or show that it does not exist.

Q: 3x2 + 1?y? + 3y? + 3z2 3 Show that lim (1,y,2)+(0,0,0) 1² + y? + z²

A: The given rational function is 3x2+x2y2+3y2+3z2x2+y2+z2. Evaluate the limit along the line y=0,z=0.…

Q: + xy² + y³ x2 + 7y² 2x3 b) lim (x,y)→(0,0)

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Q: xY Let f(x, y) and let L = lim(z,9)→(0,0) f(x, y). Which of the following 4x2 + 3y2 statements is…

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Q: lim (4x – 3y)= -11 Prove that (r.,v(-2,1)"

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Q: does not exist

A: Given that:  The limit   lim(x,y)→(0, 0 ) x2 + yx2 + y2   .

Q: Vx-2 lim х-2+ Vx2-4

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Q: Show that x²y + x² lim (x,y) →(0,-1) 24+ (y + 1)² does not exist.

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Q: xy Let f(x, y) : and let L = lim(2,y)>(0,0) f(x, y). Which of the 8x2 + 9y2 following statements is…

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Q: ху (x, y)→(0, 0) x² + y² 16. Determine whether lim exists.

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Q: 2x*y lim (x,y)→(0,0) x8 + 6y²

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Q: F (x, y) = 2xy(x²-y²) x2+y2 1) Find lim f (x, y) when (x, y) (0,0)

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Q: Evaluate lim (x,y) →(0,0) x³ +35x² + 7y²2 5x² + y² 11

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Q: 46. lim h→0 (x + h)³ - x³ h bluow

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Q: x² sin x (x, y) (0,0) x² + y² Determine whether lim exists.

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Q: Find lim (x,y)-(0,0) y7x⁹8x97y8 + x105 xy7 +x8

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Q: х2 + 2у lim (х.у)-(0.0) 1 — е*-у!

A: Explained below

Q: Find Lim-0.0 (r² + y²) In(x² +y²) '(xy)(0,0)

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Q: 16-x2| (a) lim (2 + x) 16-x²| ズ→4+ 4-x

A: Given query is to find the limit of the expression.

Q: (x-y)2 Show that lim does not exist. (x,y)→(0,0) x²+y2

A: We have to find the limit.

Q: xy cos.x f(x, y) =+3y²

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Q: ry Let f(r, y) : and let L lim(z,9) (0,0) f(r, y). Which of the following statements is correct? %3D…

A: Here we check the limit of given function using path y = mx.

Q: xy+xz + yz lim (x, y, z)- (0, 0, 0) x2 + y2 + z2

A: The given limit is limx, y, z→0,0, 0xy+xz+yzx2+y2+z2. We have to find the given limit.

Q: lim (x, y) → (4, -2) x2y + xy2 x? – y2

A: The given expression of the limit is: lim(x,y)→(4,-2)x2y+xy2x2-y2

Q: Find lim (x2 + y?)ln(x² + y?) (x,y)-(0,0)

A: To findlim(x,y)→(0,0)(x2+y2)ln(x2+y2)