Once you know limx →a+ ƒ(x) and limx →a- ƒ(x) at an interior point of the domain of ƒ, do you then know limx →a ƒ(x)? Give reasons for your answer.

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

A: Given

Q: What is lim1 f (x) ? X

A: Find your answer below

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: Find the limits a) lim x2 - 4x + 3 x2 - 1 when x approaches 1 b) lim 6x + 100 7x2 100 when x…

A: We have to find the limit

Q: Use the Squeeze Theorem to find limx→c f(x).

A: Given that 4-x2≤f(x)≤4+x2 To find the limit of the function using the Squeeze theorem when x→c=0.

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: x² – 1 lim x→1 x – 1

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Q: What is lim ? X-0+ x

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Q: Find limx→−∞(x2 −1)e4x. Show work.

A: We need to find : limx→-∞(x2-1)e4x

Q: Find the limits limx→ -∞tan-1 x

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Q: If −x2 − x + 1 ≤ g(x) ≤ x2 − x + 1 for all x does not =0, what is lim x→0 g(x)?

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

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

A: Given that f(x) is an odd function.  So, f(-x)= -f(x) Given that lim x →0+ ƒ(x) = 3

Q: a. Evaluate limx→5 f(x), where f(x) = { 11x+ (2 +77) Ef x5 f(x) exists.

A: solution is given below..

Q: Find a number b such that lim- .2. x²-4 =2 x-b x-x -2

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Q: Let ƒ(x) = (x2 - 9)/(x + 3). a. Make a table of the values of ƒ at the points x = -3.1, -3.01,…

A: Simplify f(x) first for x not equal to -3 x y -3.1 -6.1 -3.01 -6.01 -3.001 -6.001…

Q: Is there a value of a for which limx1 3x^2+ax+a+3/x^2+x-2 exists? Enter the value of a if such a…

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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: What is lim )-7(0) if f(x) = 2x2 + 1? x-0 The limit does not exist. 1

A: Solve for the limit

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: Find the limit of the function lim x → − 2 ( 2 − | x | 2 + x )

A: Topic:- calculus

Q: Find the limits limx→1+x1/(x-1)

A: limx→1+xx-1

Q: Let ƒ(x) = (x2 - 1)/( | x| - 1). Make tables of the values of ƒ at values of x that approach c = -1…

A: Make tables of the values of ƒ at values of x .

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: Find the limit: limx 1(x2 + x + 2)/( x + 1)

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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: Find the limit. y 6- 5- 4 3- 2 1- 3-2 -1 -1 1\2 3 4 5 -2t limz-0 f (x)

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Q: Find the limit. (a) lim x→3 Vx +6 – x x3 – 3x2

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Q: Evaluate the limit  Limx->0 (ex-1-x)/x3

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Q: Which property of f(x) = x' allows us to conclude that lim x- 8?

A: f(x)=x3 is a continuous function. So, it is continuous at x=2 also.

Q: 10. lim 2-と is A. -1

A: we have to find the value of the given  limit  lim    x→-∞2-x2x

Q: The function f(x) of the below graph is discontinuous at x = -1 because: a) f(-1) does not exist b)…

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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: use f(x) to find: limx→0f(x), limx→-4f(x), limx→5+f(x), limx→-4-f(x). the discontinuity that is…

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

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Q: Let flx)= S2x-1 if x>3 what is lim f(x) ? 2x+2ifX<3, what is lim flx)? メ-3 とラメふとす

A: Given: fx=2x-1if x&gt;3x+2if x≤3

Q: Find the limit of the function algebraically. x2 + 2x lim

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Q: Find the limits limx→0+x tan (π/2 - x)

A: Given that, f(x)=x tan (π/2 - x) We have to find, limx→0+xtanπ2-x

Q: Find the limit or show that it does not exist. lim √25t² + 2 − 5t t-x

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Q: f(x) is discontinuous at x=c, then  limx→c-  f(x) ≠ limx→c+ f(x) True or False?

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Q: Let f(x) = x^2 − 10x. If you construct an ϵ-δ proof to show that limx→5 f(x) = −25, what is the…

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Q: Q2: Use lim x 0 and lim x 0 to show that lim x = 0.

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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…

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Q: Use numerical evidence to estimate the value of the limit to at least 2 decimal places. x² + 2x - 48…

A: Solution:

Q: Give a specific example of f(x) with limx→∞ f(x)=1 and limx→∞ g(x)=∞ such that limx→∞ f(x)^g(x)=0.…

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

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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.