1. Evaluate the limit: ху — у lim (x, y) → (1, 2) xr - x+2xy – 2y

Q: Prove that lim 12 √16x +9y¹2 2 6 4x² +3y does not exist by showing that the limits along different…

A: We have to prove that  limx, y→0, 0 16x4+9y124x2+3y6 does not exist.

Q: Compute the limit, or show that it does not exist: lim (x,y)→(0,0) x³y? + x²y³ x4 + y4

A: To Determine :-  Compute the limit or show that it does not exist : lim x , y →  0 , 0 x3 y2 + x2…

Q: 2x? +3y2 Let f(x, y) = Set y = mx and show that the resulting ху limit depends on m, and therefore…

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Q: 4 Find the limit: lim t+0 t 4 et – 1, (Enter undefined if the limit does not exist.)

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Q: 1. Show the limit lim (r.y) ›(0,0) I 6 +y² does not exist

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Q: Show that the limit does not exist. (x + y)² lim (7,y)→(0,0) x² + y²

A: We have to check

Q: C. Prove that the limit does not exist. 1. lim (xy)-(0,0) x*+3y

A: We need to prove that limit does not exist.Below find the details solution in image.

Q: 2] Show that the limit does not exist by considering the limits as (x, y) → (0, 0) along the…

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Q: Calculate the following limit: lim (x,y) →(-1,1) 3y² + 3xy - x - y x³ + y³

A: Given, limx, y→-1, 13x2+3xy-x-yx3+y3

Q: Find the limit, if it exists, or type DNE if it does not exist. A. lim (lz²13y) (z,y) ( 3, 3)

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Q: Find lim (x,y,z)-(0,0,0) x²+y2+z4 xy+yz?+xz2 if it exists, or show that the limit does not exist.

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

A: See the attachment

Q: Investigate whether the limit exists lim (r,y)→(0,0) x²y² + (x – y)²

A: Given :                           lim(x,y)→(0,0) x2y2x2y2+(x-y)2  To find :…

Q: Find the limit lim (a,y) (-45,9) xy cos(x + 5y) (Enter 'DNE' if the limit does not exist)

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Q: Find the limit. lim zey cos 2x cos 2x P-(T.0,2)

A: limx, y, z→π, 0, 2ze3ycos2xPlug in the value x, y, z=π, 0, 2=2e3· 0cos2π=2

Q: Evaluate the limit 3(y²1) lim y 4 7y²(y-1)³

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Q: Please

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Q: Let f (x, y) = xy/(x2 + y2). Show that f (x, y) approaches zeroalong the x- and y-axes. Then prove…

A: Given :                     lim(x,y)→(0,0) xyx2+y2          We know that if the limit exist, all…

Q: For a certain function f(x, y). lim-0 f(t, 0) = 0 and lim 0 f(t, 3t) = 0. Does this mean that the…

A: Given- For a certain function fx,y it is given that limt→0ft,0=0 and limt→0ft,3t=0  To Check- If the…

Q: Show that the limit does not exist. (x + y)² lim (1,y)→(0,0) x² + y²

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Q: lim Z-y)-(0,0) z4+y?

A: To determine the limits of a multivariate function , Convert the limits into one variable and then…

Q: Q4 (а) Evaluate the limit lim xy cos y if it exist. If not, show that the limit does not (x,y)¬(0,0)…

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Q: 5) a) If a > 0, compute lim a¯*. b) Which approaches its limit faster as x→», y=2* or y=x²?

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Q: Find lim(r,y)→(0,0) ry" Cos y if it exists or show that the limit does not exist:

A: Solution :-

Q: |Suppose that dy = y3 + y? – 9y – 9 dx %3D and that the point (13, –2) lies on the graph of (x, y).…

A: Given:dydx=y3+y2-9y-913,-2 lies on the graphTo find limx→-∞y

Q: Let f(x, y) = xy /(x 2 + y2). Show that f(x, y) approaches zero along the x- and y-axes. Then prove…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Determine the value of the following limit and show that it exists. lim (x,y)→(0,0) x2 + y?

A: If left hand limit and right hand limit is equal between the squeezed function then the limit…

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: Evaluate the limit sin(a – Vy) lim (2,y)→(1,1) x - y

A: Here, we will use the following formulas,

Q: c- Show that the following limit does not exist (x² - y²) lim (x,y)-(0,0) x2 + y² 2

A: Given ; lim(x, y) -(0,0)[(x2-y2)/(x2+y2)]2.

Q: Show that the limit does not exist: (y² + x – 1)² - lim (x,y)→(1,0) (x – 1)2 + y4

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Q: Show that the limit does not exist. xy? - 1 lim (Ky)→(1,1) y-1

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Q: 1) Show that the limit doesn't exists : ysinx 3) lim (x.y)-(0,0) x²+y2

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Q: lim cos x*/x x→0

A: Given,          limx→0cosx1x

Q: Find the limit. lim (x,y) → (1,−4) 3x²y 2 1+xy²

A: I am attaching image so that you understand each and every step.

Q: 1) Show that the limit doesn't exists : 3x2 Jy 2). lim (x,y)→(0,0) x2 +y²

A: We have considered different paths y = mx. If the limit is independent of m then the limit shall…

Q: 1. Evaluate the limit: xy - y lim (x, y) → (1, 2) x² - x+2xy - 2y

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Q: Show that the limit lim (r.y)(0,0) In(1 – a²) + yª r² + y does not exist.

A: First replace y=mx and then find the limit if the limit is dependent on m then the limit doesn't…

Q: Show that the limit xłycosy lim (x.y)→(0,0) 2x4 +y² does not exist.

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Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x²yeY (x, y) → (0, 0) x4…

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Q: 1. Calculate the limit numerically. lim(x + 11) x→2

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Q: Determine lim In/xy. (x,y)(e4)

A: lim(x,y)->(e2,4)lnxy

Q: 8. Let f(x, y) be the function x3 + y3 xy? Show that the limit lim(9)→(0,0) f (x, y) does not exist…

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Q: 2. Determine the value of the following limit along all paths through the origin for which x + -2y.…

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Q: Find the limit: 1+y² In lim (x,y)→(1,0) l22+xy/

A: Topic:- limits

Q: 2. Find the limit using Squeeze theorem 1 lim,2|a – 2| sin( `x – 2

A: Given: limx→2x-2sin1x-2

Q: Suppose lim g(x) = 4, lim f(x) = 0, lim h(x) = -5. %3D Xa Xa Find following limits if they exist.…

A: It is given that,  limx→ag(x)=4,  limx→af(x)=0,  limx→ah(x)=-5 we have to solve, 4) limx→ag(x)f(x)5)…

Q: Let f(x,y,z)=x^2+4y^2+2z^2. Does the limit lim_(0,0,0)f(x,y,z) exist? If so, use generalized to 3…

A: Given:-             Let f(x,y,z)=x2+4y2+2z2. Does the limit lim_(0,0,0)f(x,y,z) exist? If so, use…

Q: What is the the value of the limit lim,0 Vn (Vn+1- /n)? Show your work.

A: