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

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: 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: 4 cos(20ax) – 4 Let a + 0. Compute the limit lim 25a2 x2

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

A: To show that the limit of a multivariable function does not exist,…

Q: 2.a²y rª + y? Show the function f(x,y) : has no limit as (x, y) → (0,0)

A: We have to show that the function fx,y=2x2yx4+y2 has no limit as x,y→0,0.

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: Find the limit. Enter DNE if the limit does not exist. lim (2,v) → (0,0) æ² + 14y²

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: Draw the phase portrait for i=2 -1. If z(0) = 1/2, what are the limits lim z(t)?

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Q: Explain why the paths y = mx and x = y² are suitable to check if the limit of %3D xy f(x,y) = as (x,…

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Q: Find the limit. Enter DNE if the limit does not exist. lim (x,y) → (0,0) x² + 12y?

A: Given limit, lim(x,y)→(0,0)x2yx2+12y2

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: Evaluate the limits in Exercise 7 and 8. cos t dt sin 8. lim x x→0+ 7. lim

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: evaluate the limit  limit as x approaches infinity of x+cos(x)/ x+1

A: To find,

Q: Find the limit of the function f(x, y) = 4e10z–3y (x, y) → (0,0). as lim (x,y)→(0,0) 4e10x-3y

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

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Q: Find the limit. lim (cos(t), cos(t), t In(t)) t-0+

A: Given: limt→0+cost, cost, t5lnt

Q: evaluate the limit of xsin(1/x) as x approaches zero using the squeeze theorem.

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

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Q: Find the limit. lim (cos(t), cos(t), t* In(t)) t-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: |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: Find the limits in Exercise

A: Given : limh→055h+4+4

Q: 3x²+2x- 3 3. prove that with the help of the limit definition (with necessary analy si)

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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: Find the limits. Enter "DNE" if the limit does not exist. lim cos (x.y)¬(0,0) x' – y' x² + y² 4x lim…

A: Find the limits : Given :            lim(x,y)→(0,0)cosx7-y7x2+y2               =  cos 0-00+0…

Q: Use the two-path test to prove that the following limit does not exist. y-2x2 lim y+x (x.y)-(0,0)

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Q: Calculate the value of the limit lim(x,y)→(0,0) 22xy/x^2+y^2 as we approach (0,0) along the path…

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Q: 2. Use the definition of the limit to prove that lim (r+2y – 1) = 1. (1,9)¬(0,1)

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Q: X,xif limF,(t)= F(t) at all t for which Fis Continuous

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: x-y (x,y) →(0.0) x + y 2.) Prove that lim does not exist.

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Q: By considering different paths, show that the limit doesn’t exist. lim (x,y)→(0,0) xy cos y/ 3x2+y2

A: Answer

Q: Find the limit. Enter DNE if the limit does not exist. lim (2,y) + (0,0) x² + 14y2

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Q: 1. Show that the limit lim (2,y)(0,0) In(1 – a2)+ y* x² + y4 does not exist.

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Q: Compute the limit (x,y)→(0,0) of 8xy / 2x^2+ 4y^2 along the following paths.   (a)  Along the…

A: Compute the limit limx,y→0,08xy2x2+4y2 along the path (a) Along the y-axis (b) Along the line y=3x…

Q: (3+4y-y is th e of lim y+ oy +3y+4)

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Q: Find the limits. Enter "DNE" if the limit does not exist. lim (z,4)→(0,0) 5x2 + 6y cos 4x + 3y + 3…

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Q: 11. Show that the limit lim (z.y)→(0,0) r² + y4 does not exists.

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Q: (4x 5y) (z,y)→(1,1) 5x2- 7y lim O 1/2 O 1/2 O Limit DNE

A: We need to evaluate the following limit limx,y→1,14x-5y5x2-7y

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: Find the limit or prove that it does not exist lim (2,y)→(0,0) T° cos x + 2y sin y x2 + 4y2

A: We will evaluate the limit limx, y→0, 0x3cos x+2y3sin yx2+4y2  using polar coordinates.

Q: 3. Compute the limit algebraically Vx +3x2 lim 6x 1

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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: Find the limit: lim f(x) as x approaches 0 of Kx2 - tan2 (mx)cos(mx)/x2     (m not =0)

A: Consider

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

A: Given: limx→2x-2sin1x-2

Q: 3. Compute the limit algebraically Vx + 3x2 lim 6x 1

A: Solution: The objective is to find the limit of the given function

Q: thát limx,y)→(0,0) x6- dõés not exist by using the two-paths approach.

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Q: compute dy/dx using the limit definition. y = 4 − x2

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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: