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 (x.y) (4,1) 2x+ y-9 6x2 lim = 3 (x.y) - (0,0) 2x2 – xy+ 1ly (x,y) (0,0) f(x) ={ x8 + x?y² is continuous at (0,0). (х,у) 3 (0,0) 1/6

Q: z2-2z+4 i) Find lim Z→1+v31 Z-1-v3i ii) z4-1 Find lim Z--i Z+i

A: The general form of a complex number is given by z=a+ib, wherea,b are two real numbers and i=-1. The…

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A: Solve the following

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Q: (2 -1) s lim z

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Q: 2.y lim (x.y)-(0.0) 12x- Show that does not exist. -1ly

A: We will show that limx, y→0, 02xy212x2-11y4 doesn't exist. One path: (along x=0)    limx, y→0,…

Q: B. Find the limit. Зх — 1 5. lim х-1/3 9х2-1 x3 - 1 6. lim х+1 х-1

A: As per our guidelines we are supposed to answer only 3 subparts

Q: What is lim x-inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^{3n}] + 2? (express answer as x,y)

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Q: 2) IF f(x) = {" (x + 2 , – 1<x<0 x, 0<x< 1 find limf(x) %3D

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A:

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

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Q: B. Find the limit. Зх— 1 5. lim х-1/3 9х2-1 x3- 1 6. lim х+1 х-1 Vx+5 -2 7. lim X→-1 х+1 Vx-1 4. lim…

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Q: (b) Prove that lim,→20,¤€A ƒ (x) exists and is equal to lim→0 Yk-

A: This problem is related to the sequence of functions. Given:  fkk∈ℕ is a sequence of functions from…

Q: 1. Show that z³+y³ lim (x, y) (0,0) 1² + y² does not exist.

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Q: Evaluate lim (x,y) ---> (0,0) (2xy^2)/(3x^2+3y^2)

A: Given term is: limx,y→0,02xy23x2+3y2

Q: Show that 4z2 z2 +1 1 (b) lim- z→1(z – 1)3 (a) lim : 43B = 00; (c) lim = 00. - - z(I – 2) 0+2 I- 2…

A: We will use the simple calculations using some usual formulae to evaluate these limits.

Q: B) Find the limits by using L.Hopital rule : x²–16 2. lim x→4 (Vx+5)-3

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

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

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Q: Vx- 2 4. lim- x-2 x2 - 4 y-1 5. lim- Vy? +3 – 2

A: We can apply the limit to the expression by applying the limit as value for the variable in the…

Q: -xy س3: أحسب lim (x,y)→(0,0) x²+y² إضافة ملف

A: See the attachment

Q: - m- J. lim x - 3 * x + 2 lim 2: *2x + 2'x² - x -6 3 m4 as x approaches m lim 2x – 12 lim x-+6 Vx –…

A: According to our guidelines, we can answer only 3 subparts of a question. Others can be reposted.

Q: 2x lim(x,y)→(0,0) x² + x + y²

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Q: Find the limits

A: To evaluate the limit: lim1x2-4 (a). When x→2+. Evaluating the limit. limx→2+1x2-4=12+2-4=10+=∞…

Q: (2) (6) xy-y-2x+2 lim (x,y) (1.1) x-1 2x-y-2 lim (xy)-(20) 2x-y-4 lim (x.y.x)-(3,4.1) (xyz) ¹√√x² +…

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Q: lim (x,y)-(-3,4) (x³ +3x²y² - 5y³ +1)

A: Here we have given an expression with limit and we have to solve it. We have lim (x,y)→(-3,4) (x3 +…

Q: (4) Find the indicated limits, if they exist: Зх—12 (a) lim→4Jx-2 x²+3x-4 (b) lim→-4 +4x x²+4x 3 cos…

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Q: 2-メ Compite lim %3D Xラム z(T-X)

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Q: X- Zx +3x+2 lim

A: Solution of question as follows

Q: (b) Show that lim (x.y)(0,0) 2x6 + y2 does not exist by letting (x, y)→(0, 0) along the curve y =…

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Q: z² +et= 1-400 2z-e² 2* - 3* 17. lim- x-0 18. lim cotxln(x+1) x-0 16. lim-

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: x2-x-2 2x-4 2sin(6x–12) 3(x-2) Sx-1 Let f(x)* ,g(x) • and h(x) Vz+2+1 a. Find lim f(x), lim g(x),…

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Q: 5. lim V2x +1 X-4 6. lim -) ズー1 x-1 CABA 3x+4 if x <-3 AT 7. lim f(x), where f(x) = 2-4 ifx2-3

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Q: lim (x,y)→(0,0) x3y is equal to----- x6+ y2 (a)1 (c)does not exist (d)-2

A: In the above problem, at the point (0,0) the function is not continuous. So, it is not possible to…

Q: -xy اس3: أحسب lim (x,y)→(0,0) x²+y2

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Q: Find the limit: 4z4 – 4y4 lim (1,9) → (3,3) 4yª z² - y?

A: lim(x, y)→(3, 3) 4x4-4y4x2-y2

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: 2. If lim x, = 1 and lim yn = 0, then it is possible to formally prove that lim(x, – Yn) = 1.

A: (Solving the 2nd question as per our guidelines) Solution of 2: The statement is "If lim xn=1 and…

Q: 19. lim x→2- x² – 4 eas y + 6 21. lim y→6+ y2 – 36 -

A: Given that limx→2- xx2-4 limx→6+y+6y2-36

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (2) limx-o x-³ (tan-¹x - x)

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Q: 2,,2 x²y² lim (x.y)→(0,0) x4 + 3y4

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Q: f(x+Ax)-f(x), Ff(x) = v2x + 1, what is the lim Дх--0 Ax

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Q: GIVEN : 2x 2х - 2x ) + 6 1 1 f (x) = 1 --x 8 g(x) = 3(x + + 4 h(x) = 6 - || 3 a.lim -4 · f (x) d.lim…

A: For (a),     limx→2-4 f(x)=limx→ 2-41-18xPlug in the value x=2=-41-18· 2=-3

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Q: V4 - x2 0sx<2 lim f(x), where f(x) = < 2 9) x-4" 2 sx<4 x = 4 B) Does not exist A) 4 C) 2 D) 0

A: f(x)=4-x20≤x&lt;222≤x&lt;44x=4

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A: Given,            limy→-39 - y23 + y + limx→-10-16*10x-4*10x + 10

Q: 3. Prove lim 3x-7= 2 X-3

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Q: x²+x5-2y lim (xy)-(3,9) %3D x-

A: Given limit lim(x,y)→(3,9)x2+xy-2yx-y

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.