1- Find the limits: Vx- 1 lim xI x-1 а. 2x3 b. lim X- o 3(x-2)2 2x3 c. lim X-2 3(x-2)2 x+1 d. lim x-3 (3-x)2

Q: Find the limits lim х2 — 1 as a. x→1+ b. x→1 c. x→-1+ d. x→-1

A: we have to find the limit    the given expression is

Q: 1. Evaluate the following limits (if it exists) (a) lim X3 Vx+6-x (b) lim ズ→1 Vx-1+x2-x ズー3 xー1 2x…

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Q: 3. Explain why the following limits do not exist. 1 (a) lim x-5 (x-5)2 -x² +3, (b) lim h(x), where…

A: (a) limx→51(x-5)2 Let  f(x)=1(x-5)2 As x approaches 5, (x-5)2 approaches 0, and so f(x) approaches…

Q: 1- Find the limits: lim V - 1 メ→ x-1 а. 2x3 b. lim x- 00 3(x-2)2 2x3 c. lim x2 3(x-2)2 x+1 d. lim…

A: Consider the limits  a.limx→1x−1x−1b.limx→∞2x33x−22c.limx→22x33x−22d.limx→3x+13−x2

Q: 2) Show that the_lim. 1) xy2 lim (x,y)→(0,0) x² +y²

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Q: Suppose that lim 4f(x)+ 2x – 14 5. Find lim f(x). z→1 %3D z→1 x – 1

A: Given

Q: 10. Find the indicated limit. x²5x - 14 lim x→7 x - 7 Show any work necessary

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Q: B. Find the value of the limit. 1. lim *+1)²(x-1) x1 x³+1 x²–4 2. lim x1 x2-3x+2 x²-4 3. lim x2 x-2

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Q: 1. Use the definition to show that x² - y² lim (x,y)→(0,0) x² - y² = 0.

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Q: 3x lim x→0 x2 + 2x

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Q: Find lim x^2 − 3x + 2/x^3 − 2x^2 as (a) x → 0+ (b) x → 2+ (c) x → 2−

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: Find the limits 4 lim x-0 x²/5

A: We know that, limx→0ax=∞; a is any of positive constant

Q: V2x + 10 + Vx² – 5x + 10 lim - X→-1 x² + 1

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Q: 4-Find the limits of the following x -1 1. lim Vx +3 - 2 Vx² +2 2. lim X+0 3x –6

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Q: 1. Evaluate the limits x* +x-12 lim x-4x-21 x -9 x-1 i. lim iii. lim- ii. x-9 iv. lim 4-3x+7x* - 5x

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Q: Q2 e valuat of the fallowing 2. ☺ lim L(x +3)t -16] xーース ☺ lim -25 X+5 メー5 lim |-X 3+X 9. X-3 メー] O…

A: To evaluate the given limits.

Q: B. Find the limit. Зх— 1 5. lim х-1/3 9х2-1 x3- 1 6. lim х+1 х-1 Vx+5 -2 7. lim X→-1 х+1 Vx-1 4. lim…

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Q: 1- Find the limits: VI- lim X X-1 а. 2x3 b. lim x→ 00 3(x-2)2 2x3 с. lim x2 3(x-2)² x+1 d. lim X-3…

A: Given: )

Q: 1- Find the limits: lim x→I x- 1 а. 2x3 b. lim x- 00 3(x-2)2 2x3 c. lim x-2 3(x-2)2 x+1 d. lim x-3…

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Q: Find the limit. . lim 2x²-x-3 X-1 x+1 . lim 2+h-vZ x-5 E lim x-5+ x2-25 . lim o. f (x) = fx³ +3 lx -…

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Q: 5. Evaluate the limit: Vx +1 lim x→1 4x -4

A: Limit at a point exists if left-handed and right-handed limits exist and they are equal. Left-handed…

Q: Find the limits of x² 1- lim Vx+1 -1 +x - 6 2- lim | x+3 x→-3

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Q: a) Find the limits: 1- lim- X-1x-x 2- lím 0 V+4-2 5x 3- lim

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Q: V2x –1 Using defination of limits, prove that lim Vx- 3 L^ = X4

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Q: Find the limits: Vx - 1 lim х>1 х — 1 a. 2x3 b. lim х- оо 3(х-2)2 2x3 с. lim х-2 3(х-2)2 x+1 d. lim…

A: Since there are multiple questions posted, we will answer the first question (1). If you want the…

Q: Find the limits 1 lim x→0 x²/3

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Q: Find the limit L. Vx - 3 1 lim X 4 X- 4 L =

A: After the substitution of limits the function gives an indeterminate form 00.

Q: Evaluate limits x - 3x +2 lim X-1 2x +x-3 lim x9x +1 i, XV

A: Here we have to elevate the limit for the given questions

Q: 3. Evaluate the following limits: +1 iv. lim 42 x-3 x+3 1 lim 4 v. 3 x2-2x-3,

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Evaluate the following limits analytically: x-2 x-1x2+x-6 a. lim 10-x-4 b. lim X--6 x+6 c. lim *+1 3…

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Q: Determine the infinite limit. x² - 4.x lim 1+4+ x2 - 8r + 16

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

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Q: 1) a) Evaluate the limit. 1 1 lim 3 x x+3 x-3

A: Introduction: The limit of a function is the base of differential calculus. When the independent…

Q: Determine the infinite limit. lim 3 sec(x) x- (T/2)+ X 00 - 00

A: Given limx→π2+3xsecx, to find the limit

Q: 1. Find the limit. x² - 25 lim x 5 x² - 8x + 15 ૨૨

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Q: (3) Find the limit. 1- x lim 1+3- X – 3

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Q: 1.) Determine the limit: a) lim vx2 + 14x + 49 x-5 b) lim (x² – 4x)³ x-1

A: Solution:To solve 1a and b1.(a)limx→5x2+14x+49(b)limx→1x2-4x3

Q: A) Find the following limits (for two only). x+1 1. limx-12-x-2 1-V 2. limx-1 1-x 2x 3. limx-0 2x2+x

A: Find the following limits.

Q: .7 Find the limit: lim .3 1 - x→1 x³ – 1 - 1

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Q: 4) Find the value of each limit: х* + х —6 а. lim х-я х — 2х-15 x→1 | Vx – 1 lim х—1 х — 1 b.

A: The limit of a function is the value of the function when the arguement of the function tends to a…

Q: show that lim(x,y)→(0,0) (x^3+xy^3/x^4+y^2) does not exist.

A: We will see that along y=mx2 path limit does not exist which means limit does not exist.

Q: Find the limit. x* – 1 - lim x→0+ In (x) +x – 1 п lim ( 1+ n

A: These question is based on Limits.

Q: 4] [2M] Determine whether the limit exist in R for lim xsin(1/x²), (x# 0). x→0

A: Zero

Q: 2/ Find the limit of the function lim X415 хъ Ч 2 X

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Q: 2. Evaluate the limits numerically. x-1 a) lim x-1 vx+3-2 x² +3x+2 b) lim x--1 x2-x-2 cos(x)-1 c)…

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Q: the limit is negative infinity enter "-INF". x2+4x-12 lim→2 x2 –4 x2 +4x–12 lim→-2 x² –4 x2 +4x–12…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: lim(x,y)->(0,0)  (4x2y)/(x2+y2)1/2

A: Given: lim(x,y)→(0,0)4x2yx2+y2         (1) To compute: The limit.

Q: Find the limit. lim(v² + x = x) = lim( Vx2 + x – x

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Q: Prove that the limit does not exist. |x – 6| lim x 6 X - 6 SOLUTION 19 – x| X - 6 lim lim x → 6+ X -…

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Q: x +1 lim а—1 х2 — 1 x-

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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.