[3 - x , x < 21 let f(x) = +1 x> 2 a) Find lim f(x) and lim X-2- f(x) X-2+ b)Dose lim f(x) exist ? why? X-2

Q: 2) lim () – X-00

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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: 3. If lim f(x) = 5 and lim f(x) = 5, what can you say about x1 X1+ lim f(x)? What can you say about…

A: Definition used -       Limit of a function -       The limit of a function at point x=a…

Q: x2 Evaluate the limit: lim 3x – 40 - - x →8 x – 8

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Q: 5. a) Explain why lim vx-3 does not exist. b) What about lim V(x 3)2 ?

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Q: The process by which we determine limits of rational functions appliesequally well to ratios…

A: Solution:Givenlimx→∞ x-34x2+25To find the limit valueFormula:ab=ab

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

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Q: 1. Find a) lim x3 3-x b) lim- x3* 3-x ,c) lim- x+3 3-x

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 3) If the lim f(x) = 2 and lim f(x) = -1 %3D x-3- x-3+ Then what is the lim f (x) = x→3 %3D a) Why?

A: To find the limit of the f(x) at x=3

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: a. Using the Sandwich Theorem to find: lim f (x) If v5 – 2x2 <f(x)< V5-

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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: x2 + x -6 2. Use the precise definition of a limit to prove lim2 x - 2

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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: Let F(x) = (x2 + 3x + 2)/(2 - | x | ). Make tables of values of F at values of x that approach c =…

A: Given: Fx=x2+3x+22-x To determine: We have to estimate limx→-2Fx by making a table of values of F at…

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: 3. Evaluate the limit: x² – 3x + 2 lim X-1 x + 1

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Q: V2x -1 Using defination of limits, prove that lim Jx- 3 L^ = x4

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Q: 4-VE Find the limit: lim→16 x-16

A: We need to evaluate the following limit limx→164-xx-16

Q: 5) Does the limit |x+1| lim x-1 x+1 exist? If yes, find its value, if not - explain why. Show all…

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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: Given that lim f(x) X+ 0 x2 1- explain why lim f(x)= ∞, x2 +7f(x)- sin (5x)+ 1 2- evaluate the limit…

A: We have to find the following

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

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Q: 5. If lim f(x) = 8 but lim f(x) does not exist, what can you X+2+ X+2 say about lim f(x)? X2-

A: We know that, limx→afx=l, if: limx→a+fx=limx→a-fx=l

Q: 4. If lim f(x) = -2, lim f(x) = 3, and f(0) = -2, what can X0+ X0- you say about lim f(x)?

A: Given, limx→0+f(x)=-2limx→0-f(x)=3f(0)=-2     Find limx→0f(x)

Q: True or false? if lim fcx) exists but Lim gx) does DぐX not exist, then lim. fox)+gox)) does…

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Q: Use lim f(x) = -2 and lim g(x) = 5 to find the limit. %3D lim [3f(x) – 4g(x)]

A: The given limits are limx→cf(x)=-2 and limx→cg(x)=5

Q: d the limit lim X-3 x-2-1 x-3

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Q: 4. What is the sign of a if f(x)= ax' +x +1 satisfies lim f(x) = 0? x→-0

A: Given that fx=ax3+x+1 satisfies limx→-∞fx=∞. Note that the given polynomial having odd degree.

Q: 1. Using L'Hospital's rule, evaluate lim(1 – x²).

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Q: Find the specified limit. x',x -1 lim f(x) - ? 2. Find the limit (if any) Jx-5 lim x-25 x- 25

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Q: Find the constant c so that the limit limx->3 (x2+x+c)/(x2-5x+6) exists.

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Q: Evaluate the limit: lim --> 0 (ex+3x)1/x

A: It is an indetermined form of questions in case of limit. Which will be solve easily by below given…

Q: find the limit or explain why it does not exist

A: Given: limx→11-x1-x for evaluating given limit, we factorize denominator and find limit

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

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Q: OUse the e, & definition of the limit to prove that: lim -4x + 5 = -3 x- 2 der: lim f(x) = L means:…

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Q: determine the limit limh→0[(x+h)2-x2]/h by treating x as a constant. determine the limx→0cos(2x)/x…

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Q: Suppose limy-e- f(x) = I and limx-e- g(x) = m. Prove that limxe-(3f (x) + 4g(x)) = 31 + 4m.

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Q: Evaluate the limits: lim x tan X- а. x→1+ b. lim x1/x X→0+

A: a)  Applying the product rule, writing limx→1+xtanπx2 as…

Q: How do you solve question 5 and 6?

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Q: c) lim -4e-x

A: c) limx→∞-4e-xlimx→∞-4ex

Q: 3. Show algebraically that lim x* – 2 – x = 0

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Q: 1. Find a) lim b) lim x→3* 3-x c) lim=-, d) the vertical asymptote of f(x)=- x→33-x 3-x

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Q: What is a limit, and what does it mean to say: lim      f(x)=1?…

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Q: Investigate the one-sided limits graphically: (a) lim x→2# x – 2 (b) lim x→0± x2 (c) lim In x x→0+

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Q: Does the limit |r +1| lim 1-1 r+1 exist? If yes, find its value, if not - explain why. Show all the…

A: We need to show that limx→ -1x+1x+1 doesn't exist. So,               limx→ -1+x+1x+1x+1 is positive…

Q: Evaluate the limit lim x² + 4x – Vx² + x ) and interprete the result in relation to x 00…

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Q: Find the limit. lim X→1 lim X→1 √√x² +15-4 2 X-1 2 x + 15 -4 X-1 || = (Type an integer or a…

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Q: Q1: b: Evaluate the limit: (1) lim-11 17-1 x-1 -2x-4 (2) lim,--23+2x² sin(x-3) (3) lim,-3²-9

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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.