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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Q: The integer n = 12700140x3243243 is missing the digit x. a) If n congruent to  3 (mod 9), then what…

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

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

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:

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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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: lim f(x, y) = 6, then f(1.9, 2.9) = 6- %3D (x, y) + (2, 3) If f(4, 5) = 3 Vf(4, 5) = (-3, 2) then…

A:

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

A:

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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A:

Q: ل بريال

A: From the graph of given function

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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…