Do the following limits exist ? If yes, find their value xy lim (x, y) (0,0) x² + y² xy lim (x, y)-(1,-1) x² + y² lim (x, y)→(0,0) theorem.) ху (Ans: No) x2 lim (x, y)→(0,0) x8 + 7y² (Ans: Yes, and the limit is) (Ans: Yes, and the limit is 0. Hint: Observe (Ans: No). y-x lim (x, y)-(1,-1) 1-y + ln(x) xy = lyl and use Squeeze

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A: According to the given information, Consider the given integer n:

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A:

Q: Given the function f(x) = 4x²-x+3, determine f(z)-f(x) Z-X a) lim Z-X b) f(x) a) lim Z-X f(z)-f(x)…

A: Given query is to perform indicated operation on the function.

Q: -x+y lim (х,у)--(1,-3) (2x + y)e¬*+y

A: Given, limx,y→1,-32x+ye-x+y To solve the above limit.

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: If lim f(x) = 2, and lim g(x) = 7 find: C→C I-C a) lim 4f(z) A C b) lim ln(g(x))

A:

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A:

Q: according to the squeeze theorem, for values of x near a if g(x)≤f(x)≤h(x) and limx→ah(x) = L then…

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Q: 1: Find the limit 6x°y5 lim (x,y)¬(0,0) x6 +y10

A: See the attachment

Q: 3) If the lim f(x) = 2 and lim f(x) = -1 %3D x-3- x-3+ Then what is the lim f (x) = x→3 %3D a) Why?

A: To find the limit of the f(x) at x=3

Q: Show that xy4 lim (x,y) →(0,0) x² + y8 does not exist.

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Q: Find the limit lim (z,y) → (0,0) 3x² + 3y² x² + y² + 16. -4)

A:

Q: (a)f(1), (6) lim→1 f(x), (c)f (2), (d) lim,→2, (e)f(3), (f) lim,→3 yA y = f(x) 4 3. -1 1 2 3 4

A:

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

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A:

Q: Which of the following statements is true? ху- 4y 1 A lim 2 (x.y) (4,0) x2-8x+y² + 16 V2x+y-3 lim…

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

A:

Q: 4. Determine the limits: a) b) 4x²-8xy lim (x,y)-(2,1) (x²-xy-2y², lim (x,y) → (0,0)…

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Q: 1.0 1.0 -1 ction f (x) : shown above. (x – 5)(x – 8)² does not exist, Þut is neither o ner -o.

A: Given function

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Q: ل بريال

A: From the graph of given function

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Q: For the function f(x,y) = (a) Find x³y 3x + y² lim f(x,y) along any straight line y = mx.…

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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: Determine the limits xy-y-7x+7 lim (x,y)→(1,4) x-1 lim x² (x,y) (0.0) x² + y²

A: 1. (x,y)→(1,4)lim​x−1xy−y−7x+7​We will factor the numerator:• Group the terms: xy - y - 7x + 7 = y(x…