evaluate the limit using continuity. 2x2 lim (х. у) -> (-2,1) 4х + у

Q: Find the limit and discuss the continuity of the function.

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Q: Evaluate the limit. lim (x,y) → (-5, -20) y² - 4xy y - 4x

A: Solve the following

Q: evaluate the limit using continuity. lim (х,у)-- (2, —1) (xy – 3x²y³)

A: Given: limx,y→2,-1  xy-3x2y3

Q: Find the limit: lim (1+x)ot=. cotz

A: L’Hopital’s Rule: L'Hospital's rule is used to evaluate indeterminate forms of limits. It states…

Q: 5 lim x-6 x + 5

A: Given Limit :           Need to find the value of limit by direct substitution

Q: Use continuity to evaluate the limit. ,2 lim 2x - 4 X→4

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Q: Estimate the limit numerically or state that the limit does not exist. If infinite, state whether…

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Q: Find the limit (if it exist).

A: Given,

Q: Find the limit (if it exists). If it does not exist, explain why.

A: lim∆x→0+x+∆x2+x+∆x-x2+x∆x

Q: Find the limit.

A: Given  The limit is limx→02+x-2x.

Q: x-2 a) limy-2+ x2–4 - 4

A: We have to find limit

Q: Evaluate the limit a x approaches positive infinity

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Q: Use L'Hoptials Rukle to find the limit of: Lim as x->-oo for (7(x^2) + 4x) / (9 - 3(x^2))

A: Solve using L'Hopitals rule

Q: Evaluate the limit using continuity.

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Q: Find the limit by rewriting the fraction first. У + 64 lim (x.y) (8, - 64) x3y- xy + 64x2 – 64x…

A: Consider,limx,y→8, -64y≠-64, x≠x2y+64x2y-xy+64x2-64xTo find: The limit of the given fraction.

Q: assume that lim (х,у) --(2,5) to find the limit. lim 8(x, y) =7 (х.у) -> (2,5) f(x, y) = 3, lim f(x,…

A: Given that, limx, y→2, 5fx, y=3    and   limx, y→2, 5gx, y=7   To find:  limx, y→2, 5fx, y2gx, y…

Q: Estimate the limit numerically or state that the limit does not exist. If infinite, state whether…

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Q: Find the limit as x--> ∞ lim In x2 O 2x 00 8.

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Q: Find the limit is it exisit.

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Q: Find the limit, if it exist の十2 lim

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Q: A- Find the limit for th 1. lim tanzx

A: (A)1. limx→0tan 2xsin 4x=limx→0sin 2xsin 4xcos 2x=limx→0sin 2x2xsin 4x4xcos 2x×12=limx→0sin…

Q: Use continuity to evaluate the limit.

A: Given: limx→45+x5+x for evaluating given limit, we substitute x=4 in given limit

Q: Find the limits by rewriting the fractions first.

A: Given: limx,y→1,1x2-y2x-y

Q: cot3x Lim X-o cotx 0

A: Given limx→0cot3xcotxTo evaluate the limit:

Q: 2. If it exists, find lim f(x) where X--1 x =-1 f(x) = { *x– 1)³, x+-1 4, If the limit does not…

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Q: Assume that lim (х, у) — (8, 6) f(x, y) = 2 and lim (х, у) — (8, 6) g(x, y) = 3 to find the limit.…

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Q: Which statement is correct? The Quotient Law does not hold if: (a) the limit of the denominator is…

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Q: Evaluate the limit 1 lim x--3 (x + 3)²

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Q: Find the limit if it exists. Lim,-2 (Væ² +5)

A: Given Lt _x->-2   (√(x²+5))

Q: Find the limit, if it exists. 4x2 lim x--0 x+ 1

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Q: Find the limit and discuss the continuity of the function.

A: Given  We need to : i) find the limit. ii) Discuss the continuity of the function.

Q: (a) lim (3x + 5) = 2, I-1

A: a limx→-13x+5=2using ∈-S definitionWe need to prove that :Given any ∈, we can find S , so that…

Q: Estimate the limit numerically or state that the limit does not exist. If infinite, state whether…

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Q: Find the limit using direct substitution. 3x + 2 lim x-1 1-X 1 -x

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Q: Find the limit. If the limit does not exist, type DNE. lim (1,9) →(-4, -2) 32 – 5zy =

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Q: Evaluate the limit, if it exists. lim((3/(y2+y))- 3/y) y-->0

A: To determine the limit of function, if exists.

Q: Find the limits by rewriting the fractions first.

A: Given limit is, lim(x,y)→(1,1)xy-y-2x+2x-1

Q: Find the limit or show that it doesn't exist. 1-х-х2 a) limx→-o 2х2-7 V1+4x6 b) limx 2-х3

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Q: What is the Reworded limit and continuity?

A: Given: limit and continuity

Q: Find the limit. lim e^(-2x) x-->∞

A: To find the limit of e^(-2x) as x tends to infinity.Check whether the L Hopital’s rule applies.

Q: Find the limit (if it exists). If it does not exist, explain why.

A: Left hand limit: Right hand limit:

Q: Find the limit, if it exists lim(2,y,2)->(0,0,0) 6+y+826

A: To find the limit

Q: Evaluate the limit using L'Hospital's rule lim 3xe 3x --

A: To evaluate the given limit using L-Hopitals rule.

Q: Evaluate the limit, if it exists. lim (1/4+1/x)/(4+x) x--> -4

A: The given expression is,

Q: Find the limit if it exists. x²+5x+6 Lim,→-3 a+3

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Q: The limit lim (x,y)→(-1,2) (x²y − 3xy²) = −8 - Select one: True False

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Q: Evaluate the limit, if it exists.

A: We have to find limit: limx→-414+1x4+x Since it is 00 indeterminate form so making it determinate by…

Q: Find the limit z° + 1³iz4 lim z→-li z10 + 110

A: