Which of the following expressions are true for the limits : 3x²y? 1 2X-y I. lim (x,y)-0,0) II. +y sin lim III. (x.y)-0,0) x*+2y" lim (x,y)→(0,0) 2+2*+y (a) I: Limit exists and the value is 1 (b) I: limit door

Q: 6 Which limit can be interpreted as 2 dx? (2+1)= dr? A. lim E (2) 2 (zk+1)° -k=1 n+00 O B. lim E (1)…

A: Given query is to find the correct option of the limit.

Q: 2) Find the limit for the following equations: a) lim (+1) x--1x²-x-2 x²-9 x-43 |x-31 b) lim

A:

Q: т? — Ох — 16 - - Evaluate the limit: lim x →4 x – 4

A: We need to evaluate the limit limx→4x2-0x-16x-4 Which is equivalent limx→4x2-16x-4…

Q: Evaluate the limit lim, 4 4x 13z-12 4-V4r Answer: dy Find for the function x'y + 5xy = 17 at the…

A:

Q: a) lim W→0 f(3+w)-f(3) W y-f(x) Fig. 10 b) lim h→0 4 ƒ(4+h)-f(4) h c) lim S-0 ƒ(5+s)-f(5) S

A: The given graph of  shows the function is discontinuous at .The given limits show the derivative of…

Q: please answer all i really need it and make sure it’s correct

A:

Q: Find the limits : x'+y° lim (x,y)→(1,-1) x +y

A: We have to find the limit: lim(x, y)→(1, -1) x3+y3x+y

Q: Evaluate 1. limit 2. limit = -3 3. limit does not exist 4. limit x+1 lim x⇒−1 x² – 3x − 4˚ 1 5.…

A: Given: limx→-1x+1x2-3x-4

Q: Find the follawing limits: 1. lim tan" メーbo 2. lim Sith)2I 3. lim 2x-3 メー 7X+4

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: lim (x,y)(2,-3) x 2.

A: We simply put limit here.

Q: 3 sin x-x The value of the limit : lim,→0 is 15x

A: limx→0 sinxx =1

Q: Ouestion 3 A. Evaluate the following limits: i. lim (3 + x)² - 9 ii. lim x² – 25 5-x iii. lim 5x+6x²…

A:

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim x-0 sin 2x x2-16 2. lim x-4 (Vx+5)-3

A:

Q: Evaluate Given Limits a. Lim (6h+h²+3) →>0 b. Limo 4h+h² 4 c. Lim (1+2h+h² +2+2h) d. Limo 2xh+h²-2h…

A:

Q: 3) Find the following limits. You must show your work. 2-x b. limcot x a. lim (x-1)

A:

Q: Show the limit does not exist by choosing two paths to the origin whose limits L1 and L2 are not the…

A:

Q: 02/Use the l'Hopital's rule to find the limits in t3-4t+15 a) lim t--3 t²-t-12 X-8x² X-00 12x²+5x b)…

A: Given problem:-

Q: ☺ use the groph of the funchion f to the following limits.and funchion values

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: = xp (x + x)T im 2 ( -i - r) . If n- co n where a, B and y are positive integers, then a + B + y = 6…

A: To find: The value of α+β+γ. Given information: If ∫-21 x2+xdx=limn→∞3n∑i=1n αi2n2-βin+γ…

Q: 7. Compute the limit to infinity: 4-2+3r+1 a lim 7+3r-r+ 12

A:

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: