x² + y² lim (x, y)→(0,0) V – 1 x² + y² + 1

Q: (#1) lim (#2) lim (x,y)(0,0) x2 + y? (1,y)(0,0) (x2 + 2y6)2

A: ggg

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

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Q: lim If (2,y)(0,0) f(x, y) = 0 then lim f(x, 0) = 0. T→0

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Q: Find the indicated limit by using the limits

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Q: z+ iz lim z+0 z+ iz equals .a None .b -i .C 1- .d i .e 1

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Q: lim h0 h x+h Vx+h-Vx lim h x > 0 h-0 25-u-5 lim u-0 v1+u-1

A: 1)…

Q: lim (1.)(0,0) r +y – a²y²"

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Q: .2 - (a) lim x + y (2,y)-(1,1) xy y+4 (b) y # -4, x 4 x lim (7.y)-(2,-4) x2y - xy+4x2- 4.x' 1 a+y-4…

A: To calculate limits by arranging fractions:(a) lim(x,y)→(1,1) x2-y2x-y=lim(x,y)→(1,1)…

Q: iz³+1 lim z--i z²+1 3 2 ylgn ihi

A: Finding the limit by l'hospital rule

Q: lim (x,y)→(0,0) (x² + x²) (х, у) ->(0,0) а. 0 b. 1 с. 1/2 d. Does not exist

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Q: X - iy Discuss the limit Lim I+0 X-1y y-0

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Q: lim y approaches 2 .............. y + 2/[y^2 + 5y + 6]

A: Given, limy→2y+2y2+5y+6 To solve the above limit.

Q: 4. Proof Prove that lim x"y" dx dy = 0. n→∞

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Q: 1. limxy)¬(2,1) 2x² + y 2. lim(xy)¬(0,0) x + 4y + 1 x+y 3. lim(x,y)→(-1,2) x-y 4. lim(xy,z)→(1,3,4)…

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Q: 3 sen y lim (xy)-(3,0)

A: Since lim(y tends to 0) sin( y)/y=1 Therefore, lim(x,y)tends to (3,0) x^3sin(y)/y=(3)^3×1=27

Q: 2 i (z-i) lim z→i z2+1 1 O 2i 1 -1

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Q: lim (x.y) (0,0) r + yt

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Q: z² + iz lim z3 + 1 z- ob ||

A: We are given : limz→∞z2+izz3+1=limz→∞z2+izz3z3+1z3=limz→∞1z+i1z21+1z3=0+i(0)1+0=0…

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

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Q: ขน lim (x,y) → (0,0) x² +10y²

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Q: Does lim (x,y)→(0,0) x² + y² y2 exist? Explain.

A: Here given  limx, y→0,0y2x2+y2

Q: 3x2 1) lim (x,y)-(0,0) x2 + y² + y2 ysinx

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Q: lim xy + 2y - 3x - 6 (x, y) 4, 3) y +3 y-3 2 O 6

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Q: lim zta sec z is A B 2 D nonexistent

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

Q: xy - Y lim(x,y)→(1,0) (x − 1)² + y²

A: Please see the below picture for detailed solution.

Q: lim (x,y)-(2,4) x² +x/F-2y x-Vy %3D ||

A: Solve the limit

Q: 2 i (z-i) lim Z. z²+1 1 O 2i 1 - 1

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Q: x4 - y4 25. lim (x,y)→(0,0) x ² + y2

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Q: lim, (V+x+1 - V+1) – Vx² x* + 1

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Q: secy-1 Lim seczy-1 a) as y → 0 b) as y – → 1/2

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Q: x' + xy² a) lim (x,y)→(0,0) x' +x x' - y² b) lim (x,y)-¬(0,0) X¯ +y x* – 2x*y + 4y² x* + 4y? c) lim…

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

A: We have to find the limit.

Q: secy-1 Lim sec2y-1 a) as y → 0 b) as y → T/2

A: To determine the value of the limit limy→0secy-1sec2y-1, apply L'Hopital's rule.…

Q: xy + 1 lim (x, y)→(1, −1) x² − y²

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Q: lim(z+z¬1) z + z¬1) ze

A: Every complex number can be written in the polar form as z=x+iyOR z=reiθ=rcosθ+i sinθwhere r=x2+y2…

Q: x - y 1. lim (x,y)¬(3,3) 1 2. lim x-0 xVx + 1

A: (1)  lim(x,y)→(3,3)x-yx-y=lim(x,y)→(3,3)x-yx-y×x+yx+y (We rationalize the denominator)…

Q: lim (x,y)→(0,0) (3 + (x² + y²) In(x² + y´

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Q: 2x-2y* If f(x,y)={3x² +3y² if (x, y) # (0,0) then: m if (x,y) =(0,0) f(x,y) is continuous at (0,0)…

A: To check whether the function is continuous or not. Given information: The function is…

Q: iz iz°+ 1 C - lim z -i z2 + 1

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Q: iz° + 1) lim z→-i\ z² 2 +1,

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Q: ry - y lim (z.y)(1,0) (z – 1)² + y²

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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: x²y 3x2 A. В. lim (x,V) - (0,0) x2 + y? 2y? lim (x,) - (0,0) > ) x² +y " x³y+x²y³ C. lim D. lim…

A: we have to find limit

Q: lim ilm f(x,y)=x²y²÷x²y² Calculate the two limits of the function

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Q: x²y²z² lim (x,y,z)→(0,0,0) x² + y2 + z²

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Q: lim (x,v)→(-2,0) g(x, y) does not exist given that Show that (x+2)³y² (x + 2)6 + 3y4' 0, if (x, y) #…

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