Vz + 2 - Vỹ (z,v)-(1,3) (z + 2) – y Evaluate lim Use two path rule to show that lim (1,y)-(0,0) 23 + 2y3 does not exist.

Q: lim ( + y) In (² + y?) (z.y)-(0,0)

A: We can write the above expression as following :' x2+y2lnx2+y2=(x4+x2y2)lnx2+y2x2. Now, if we put…

Q: What is lim f(z) z→1 9(2) given f(x) = e2" and g(x) 3x2 – 3x + 6 ?

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Q: 2f(x)=x² x-1 f(x)+1 3. If lim f(x) = 2, what is the value of lim a) 0 b) 1 ? c) 2 d)

A: Given: Limit ( x-> 1) f(x) = 2  Need to find- Limit ( x-> 1) [ 2f(x) - x2 / f(x) + 1 ]

Q: 2x*y lim (x,y)→(0,0) x8 + 6y²

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Q: x³ + 4y³ lim (x,y) (0,0) x² + y² x³ + 4y² lim (x,y) (0,0) x² + y² lim (x,y) →(1,1) 13x³ + 5y² x² +…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: (a)f(1), (6) lim→1 f(x), (c)f (2), (d) lim,→2, (e)f(3), (f) lim,→3 yA y = f(x) 4 3. -1 1 2 3 4

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Q: (4) lim √ x — + x +5 x→4 (Ans. 5

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Q: 4-ху Find lim (x,y)¬(2,1) x²+3y2 if it exists, or show that the limit does not exist.

A: limx, y→2, 14-xyx2+3y2Plug in the value x, y=2, 1=4-2· 122+3· 12=27

Q: limx→o (t+1)f(t)dt Assume f (0) = 4 %3D 3x2

A: Explanation of the answer is as follows

Q: F (x, y) = 2xy(x²-y²) x2+y2 1) Find lim f (x, y) when (x, y) (0,0)

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Q: Find lim (x,y) →(7,0) 7x - 5y #49 √7x-5y-7 7x - 5y-49 by rewriting the fraction first.

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Q: Зп + 6ni ) lim n0 |2+ 3i|n

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Q: find the domain (d) , range (r ) and asympote (a) of the graphof the function f(x) = (3/5) ^6x  A.…

A: Given function is  fx=356x The domain, range and asymptote of the graph of the function are…

Q: x²-1 2. limx-1 1-x

A: Since you have asked multiple questions in a single request so we will be answering only first…

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: (a) Find fave of f (x) fave i = 2x over [0, 6]. e Textbook and Media

A: We do only first part of multiple questions.Given,.We know that the formula of average value of…

Q: Show that when T(z) = az+b cz+d where (ad - bc ‡ 0), find lim T(z) = ∞ if c = 0. 7-3

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Q: x+vy-1 (a) lim (x.y)-(1,0) (x-1)²-y (b) lim 4x² -5y²-z² (x.y.z)→(1,0,1) 4x²-5y²+z2 (c) lim…

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Q: secies to find lim use

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Q: K Given the function f(x) = 4x2-x+ 3, determine: f(z)-f(x) Z-X a) lim Z→X b) f(x) a) lim Z→X…

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Q: limy 2y³ + 5y² -7 00 10y³ – 9y+12

A: limy→∞2y3+5y2-710y3-9y+12

Q: x² – y + 1 f (x, y) x² – y? + 1 -

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Q: Find x² + 5y²-5 lim 2 (x,y) →(5,2) x² + y² +3 x² + 5y² - 5 lim (x,y) →(5,2) x² + y² +3 2 (Type an…

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Q: x = a = x + x²y y=b-x²y. Here a, b 0 are dimensionless parameters and x, y> 0 are dimensionless…

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Q: b) Find the limit, if it exists, or show that the limit does not exist. 3x4 - 3y4 lim (x,y) (0,0)…

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Q: x²-y² lim (x,y)→(−1,1) x²−xy−2y²

A: Approach to solving the question: To find the limit lim⁡(x,y)→(−1,1) x²−xy−2y²x²−y²​ , we need to…

Q: x- 2 x→2 J4x +1-3 evaluate lim (No estimation, no l'Hopital's rule)

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Q: Q1: Using the function, find u(v(f(x)) if u(x) = 4x – 5, v(x) = x² and f(x) =

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: f(8+ h)-f(8) lim h-0 where f(x) = 2x + 5. If the limit does not exist enter DNE. Limit =

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