Q1. xy+4 i. Evaluate lim(x.y)-(0,2) x2+y2 ii. If x + y = 2e® coso and x- y = 2v-1 e® sing then show that azu 4ху дхду a2u a2u a02

Q: 3x2 + 1?y? + 3y? + 3z2 3 Show that lim (1,y,2)+(0,0,0) 1² + y? + z²

A: The given rational function is 3x2+x2y2+3y2+3z2x2+y2+z2. Evaluate the limit along the line y=0,z=0.…

Q: QI/ Find the following 1. lim + 2 = 3 2. lim (5x – 4 +)

A: Simplification of the function and substitution of the point of limit helps to find the required…

Q: 3. lim,10 Vx – 1

A: The limit of any function is defined for any function F(x) on any interval that contains point at…

Q: lim a. b. lim t-2 V2 + t – 2 t – 2 sin 7r с. lim 50 sin 3r 8 d. lim 16 16. V9r² + 4 lim 2.r + 1 е.

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Q: 2 lim y² - 7y + 12 3 y → 4 y - 64 1 48.

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Q: Evaluate using the identity a3-b3 = (a-b)(a2+ab+b2)

A:

Q: 1. lim→- Зx? (2х - 1) 1 + 4x + 3 9. limx--3 x2- 3 2.

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Q: 1 I 4 x 4 x 4 49. lim-

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Q: 04 Evaluat the allowing Limits メニ1 Lim メー→」 メート Lim 4メー2x+ 3x-5 メー

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Q: Evaluate: lim x→-1 x² + 2x + 1

A: Limit: Limit is a mathematical concept based on the concept of proximity that is used to give values…

Q: 3. (x +2 ) Ex²-4)

A: y=(x+2)3x2-4

Q: (3х-5) 9. lim x--1+ x+1

A: This is a question of limit of the function. First we will try to convert this function into most…

Q: Evaluate  -3 to 3 ,  0 to (9-x^2)^1/2   and  ∫∫sin(x^2+y^2)dydx.

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Q: 2х+3 5. lim X→00 5x+7

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.