Let f(x, y) : and let L = lim( y)>(0,0) f(x, y). Which of the following 9x2 + 3y2 statements is correct? O L=0 O L=1/12 O L does not exist because f(x,y) is not defined at (0,0). O L does not exist because the limit as (x,y) goes to (0,0) along the x-axis is different from the one along the y-axis.

Q: The function f is defined by f (x) = x² sin. The application of the squeeze theorem guarantees that…

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Q: II. Prove that for each of the following lim (x,y)→(0,0) f(x, y) does not exist. ,2,,2 4. f(x,y) x4…

A: limx, y→0, 0x2y2x4+y4

Q: 2. Use the ɛ-d definition of the limit of a function to prove that lim = 3. I-»3 T – 2

A: Let  I  be an open interval containing  c , and let  f  be a function defined on  I , except…

Q: 1. Let Evaluate the following limit. 7 (t) = (t² + 5, t²-5t+6 t²-9 lim r(t). t-3 > sin(πt)).

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Q: Use the e – 8 defintion of a limit to show that lim (6z – 4) = 2+ 6i z→1+i

A: The given problem is to show and evaluate the given complex limit by using the epsilon-delta…

Q: 6. Compute the following limits. ry (a) lim (z.) >(0,0) 3r² + y6° 3r2 – 7ry + 2y² I – 2y (b) lim…

A: Ans A):

Q: sin(r – 3) lim I3 r2 + 2r – 15

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Q: 5. Determine the infinite limit. a). f(x) = lim +1 x-5 2-t b). ƒ(t) = lim t→1 (t–1)2 x→5-

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Q: Suppose that f: R→R is a continuous function, satisfying f(5)=8. What is the value of the limit lim…

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Q: 5. Find the limit or show that it does not exist. sin(x – 1) lim 2 x→1 x´ + x -2

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Q: 1. Evaluate the following limits: 2²+y? (a) lim(,y)→(1,–1) 2ry (b) lim(z,y)→(2,1) 3r+3y2 (c)…

A: According to our guidelines we can only answer 1 question or 3 subparts only, rest you can repost

Q: 2ry? does not exist. now that the limit lim (z,y)+(0,0) x² + y!

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Q: Find the limit of f (x) = √(14 + √x), defined on X = [1, ∞)

A: The given function is: f(x)=14+x  is defined on [1,∞).

Q: (c) x² - y² lim 2 (x,y) →→(0,0) x² + y² 2

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Q: Find the limits 2 lim as (x – 1)2/3 a. x→0+ b. x→0 c. x→1+ с. d. x→F

A: Given function is fx=1x23+2x-123

Q: Use the Squeeze Theorem to evaluate the limit lim f(x), if 17 Enter DNE if the limit does not exist.…

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Q: 12. Given f(x)=x² – 4x – 5. Find lim fx) –{2) x-2 2

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Q: 5. Use the definition of limit to prove that lim[(x – 1)(sin x²)] = 0

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Q: Evaluate the following limits: x² – 4 -5x + 2 I – 1 (i) · lim 2+2 x2 + x – 6. . (ii) I¬∞ 5x² + 2x +…

A: (b) (i)

Q: 2. Find the limit using Squeeze theorem 1 lim-2|x – 2| sin( r - 2

A: Squeeze Theorem- Let f, g and h be functions defined on an interval I. Let c∈I be its limit point.…

Q: 4. Find the following limits or determine that they do not exist: 1+1/x a. lim,-0 1+1/x² 1+1/x? b.…

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Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: