Fill in each blank so that lim f(x) exists x→2 1 Ex+1, x < 2, _, x < 2, f(x) =- x + f(x) = {2 3x +_ r2 2. -x +6, x > 2. x² -5.x+6 x² – 9, x< 2, x<2, f(x)=- f(x)={ x- 2 -x + r2 2. x>2.

Q: # 3) lim (2x - 4x2 - 5x+6) X→-3

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Q: Show that lim(5x+2)=-18 x-> -4

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Q: lim, →2, 1 X – 2J2x

A: The limit of the function is given limx→21x-2∫2xx2dt1+t3. To check the limit of the function ,…

Q: find lim ( 3x2 -2x -1) X --> -1

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Q: Prove that limxS2 ƒ(x) = 4 if

A: Given that : The function is f(x) =x2,    x≠21  ,    x = 2 .

Q: 6х2+1 2. Find lim X→0 V4x4+3x+1

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Q: If 2x - 2s f(x) sx² - 2x + 2 for x 2 0, find lim f(x). x-2

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Q: V7x* +4x' -x² -2 lim x³ - 2x² -3x+1 4x-x²-2 x -0

A: Solution:

Q: x* +x² – 1 limx→c x²+5

A:

Q: 1. Find the value of the expression lim x²+x+21 X-3 x-1

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Q: -2x² + x 41. g(x) y 3 - 1 -2 - 1 (a) lim g(x) (b) lim g(x) *→-' 1.

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

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

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Q: 2х -2х 5e — Зе - lim 2х -2х 2e +e x → -00

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Q: If a function where limx→1+f(x)=3 and limx→1−f(x)=3, thenf(1)=3   true or false, if false make a…

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Q: (3x-1)² - lim x→1 (x+1)3

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Q: Find 2-Vx2-5 lim X-1 x+3

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Q: (x+2)2 - 4(x+5) limx x- 4

A: Given,             limx→4x+22-4x+5x-4

Q: 1 c) lim x+0 \ex-1 X.

A: the given expression is: limx→01ex-1-1x…

Q: Guess the value of lim x 0 (tanx-x)/x3

A: Given :          limx→0tanx-xx3

Q: lim (2x-5x) is x--2

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Q: d) (x+27) -3 X lim-

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Q: f-x² + 10x - 25 < g(x) < a² - < 10x + 25 for 4 <x 6, evaluate lim, →5 9(x).

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Q: 4x + 1 x + 5x a. lim 8x - x - 6 x ( 3x - 4) b. lim Зх + 9 3x 4x - 7 lim С.

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Q: If f(x) = 5x² − 5x + 31, evaluate lim_f(9 + h) − f(9) h→0 h If an answer does not exist, enter DNE.

A: given

Q: Calculate lim X→-2 x³ + 2x² - 1 5 - 3x

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Q: 7) lim (-2x3 + 3x-1) X=00

A: We have to find limx→−∞​(−2x3+3x−1).By applying Infinity Property that…

Q: Graph of y = B(t) y = B(1) a) Evaluate lim B(t). t-2+ b) Evaluate 奥B(). →2- c) Evaluate B(2)

A: Topic - value of limit of function From graph Note - as per bartleby Guidelines We are supposed To…

Q: x*+x3 2. Calculate lim x→0 12x3+128

A: limx→∞x4+x312x3+128

Q: 7. lim (x2 + 1)i – x

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Q: 5x – 1, {2x² – 3, x 3 -

A: Given: The function, fx=5x-1,       x&lt;32x2-3,      x≥3.

Q: Evaluate V1+ sin x V1+ tan x lim x→0 - x3

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Q: Calculate limx→∞x3+3x+52x3−6x+1.

A: We have to calculatelimx→∞x3+3x+52x3-6x+1

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.