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 f(1)?

Q: Find limit of lim x-->0 of f(x)= (e3x-3x-1)/(4x^2

A: Given limx→0e3x-3x-14x2

Q: the limits if it exists, if it does not explain why. (1) lim ()" (ii) lim

A:

Q: Suppose that limx→2[f(x)+x2]=α. Find  limx→1(x+1)f(2x) 2α−4 Not applicable  2f(2) 2(α−4)

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Q: 2. Construct a table of values to investigate 1 if x -1

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Q: lim (In(x))½ ?

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Q: 7. If you know in advance that lim f (x) exists, can you determine its x→5 value just knowing the…

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Q: x2 +1 Can L'Hôpital's Rule be applied to lim x→1 2x + 1

A: To check if the L'Hospital's Rule can be applied or not, first we need to find the limit by directly…

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

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Q: Suppose that on the interval (2,5) f(x) less than or equal to g (x) less or equal to h (x) and Lim…

A: We have the following information.

Q: 32. lim x + x - 2 x2 - 1 2,

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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: (a) lim n-0 2 – ni x² – 4 (b) lim x + 4 x² – 4 (c) lim x – 2

A:

Q: lim f(x) x--> 3, where f(x) = {2(x+1), if x < 3 or 4, if x = 3, or x^2 - 1, if x > 3}…

A: First we find the limit of f(x) from left side and right side .

Q: If lim f(x)=-2 and lim g(x) = 2, what is the value of lim [f (x)+2g(x)]?

A: Given, limx→afx=-2  and  limx→agx=2

Q: Once you know lim x-->a+ f(x)  and lim x-->a-  ƒ(x) at an interior point of the domain of ƒ,…

A: If we know the right and left-hand limit of a point then we know the limit at that point.

Q: (a) lim x→2 arctan(7-3x)-" 2х-4 4 (b) 10-e5x lim x→00 16-x2

A: See the calculation and explanation below

Q: Suppose that a function f(x) is defined for all real values of x except at r = c. Does it imply the…

A: Here we have to check whether the limit exists or not.

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: Q1/ Find the following 1. lim x2 + 1 = 2 x00 (x-2)2 2. lim x-2 (x-2)(x+2) 3. lim (5 -) x-0

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Q: lim x yields to 1  x-1/(square root of 4x +5)-3

A: As the given limit is not legible, the limit is computed in 2 cases. Obtain the limit as follows.

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: If Lim [x3 – g(x)] = 12 as x tends to 3, use the Rules of Limits to find Lim g(x) as x tends to 3.…

A: Given: limx→3x3-gx=12

Q: 2) Find lim f(x). X→1 f(x> X 2. 2.

A: here      limx→1- f(x)=1    and            limx→1+ f(x)=2 here                            limx→1-…

Q: Q \ Find the value of 8 > 0 that guarantee lim x-0 csc(1/x) = 0 in terms of ɛ?

A: Definition of limit: We know that, limx→af(x)=L               ...(i) For each ϵ>0, there exists a…

Q: 1. Evaluate the limit: 5 - x lim x→5+ (x – 5)2

A: Since you have asked multiple questions, we will solve the first question for you. If youwant any…

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: If lim f(x) =5 x-->1- and lim f(x)=5 x-->1+, what can you say about lim f(x) x-->1? What can you say…

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Q: . Is it possible that f(2) = 5 but limx→2 f(x) = 7? If so, what kind of function can satisfy this?

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

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Q: F(x)={tan(x+3) x3-) f(x) Photo better depicts problem, thank you!

A: Given,           Fx=tanx+3x<-3x+33+1-3≤x

Q: Suppose that ƒ is an odd function of x. Does knowing that lim x-->0+ ƒ(x) = 3 tell you anything…

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Q: If lim (x approaches 6) (f(x)-4)/(x-3)= 2, how do I find lim (x approaches 6) f(x)?

A: We separate the limit first.

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: Given f(x) = 2x^2 + x -15 all divided by x+3 find lim x -> -3^f(x) algebraically is f(x) continous…

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

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Q: Q1) Find lim Bx+4-4cos²x+tanx x-0 4sin2x 10x2+125-5 Q2) Find lim x-0 3x2

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Q: 2. If lim x, = 1 and lim yn = 0, then it is possible to formally prove that lim(x, – Yn) = 1.

A: (Solving the 2nd question as per our guidelines) Solution of 2: The statement is "If lim xn=1 and…

Q: 9. Build a table to estimate lim sin 1 (Hint: Use multiples of T) (x³ – 3x2 + +6– 2x) 10. Use a…

A: As per the guidelines we are suppose to answer only one question. Please repost the remaining…

Q: Evaluate lim (e* – 2.x) x→0-

A: To evaluate: limx→0-(e3x-2x)3x

Q: If lim x→5+ f(x) = 11 and lim x→5− f(x) = 23, then what (if anything) does that tell you about…

A:

Q: 3- If lim f(x) = 3.5 and lim,2+ f(x) = 6.5 , the function has a double sided x-2- limit or one sided…

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Q: c) lim -4e-x

A: c) limx→∞-4e-xlimx→∞-4ex

Q: —ах+6 if x2-1 Let f(x)=< For what value of a does 2x2 +ах ifx<-1 lim f(x) exist? x--1

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Q: f(x+Ax)-f(x), Ff(x) = v2x + 1, what is the lim Дх--0 Ax

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Q: Find the limit.

A: Given,

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

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Q: 6 Find the value of a such that 2x2 - ах — 14 lim х-1 х2 — 2х — 3 exists, What is the value of the…

A: The limit of a function at a point 'a' in its domain is the value that the function approaches as…

Q: Use l'Hospital's rule to find the limit.  lim x→0  ex − 1 − x x2

A:

Q: Evaluate A) lim x͢ 1 2 x2 + 5x + 7. B) limx͢.-4 (√x2 + 9 – 5)/(x+4

A: Consider the given limit: A) limx→12x2+5x+7B) limx→-4x2+9-5x+4 Here, the objective is to find the…

Q: What type of discontinuity is at x = 3, if lim f (x)= 0 and lim f (x)= 0? x-3 x>3* What type of…

A: