Explain what it means to say that lim f(x) = 1 and lim f(x) = 3. x → 2- x - 2+ O As x approaches 2 from the right, f(x) approaches 1. As x approaches 2 from the left, f(x) approaches 3. O As x approaches 2, f(x) approaches 1, but f(2) = 3. O As x approaches 2, f(x) approaches 3, but f(2) = 1. O As x approaches 2 from the left, f(x) approaches 1. As x approaches 2 from the right, f(x) approaches 3.

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: Explain why the following limits of (a) and (b) do not exist. (a) lim - x→1x-1 sin x (b) lim x→1…

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Q: Consider f(x)=x−9/x+4 a) As x→∞, f(x)→ b) As x→−∞, f(x)→ f(x)=10x+7/x−6 c)limx→∞f(x)=

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Q: Show directly from definition that if lim,l- f(x) = 2 and lim,1- 9(z) = 3, then lim,1- f(r) + g(x) =…

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Q: Evaluate lim f(x), where f(x) = e value of "p" assuming that lim f(x) exists. Nx + (M + 77) if x<5…

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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: Determine whether f(x) approaches o or -o as x approaches 5 from the left and from the right. -1…

A: fx=-1x-52=limx→5--1x-52=limh→0-15-h-52=limh→0-1h2=-∞

Q: 1. For reference, write down a formal definition for lim f(x) = L.

A: The epsilon-delta definition of limits says that the limit of f(x) at x=a is L if for any ε&gt;0…

Q: If lim as f(x)-4/x-3=2 as x approaches 5, find lim f(x) as x approaches 5.

A: We have

Q: Let f(x) = (1 + x)1/x. (a) Estimate the value of the limit lim (1 + x)1/x to five decimal places.…

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Q: Explain what it means to say that lim f(x) = 7 and X 3 lim (x) = 9. X 3* %3D %3D O As x approaches…

A: To Determine: explain what it means to say that options are given  Given: we have limx→3-f(x)=7  and…

Q: In terms of limits, what does it mean for f to grow faster than g as x→∞? Choose the correct answer…

A: We need to choose correct option.

Q: Find the value of lim f(x) 1 f(x)3= 1+5/x -0.6 -0.5 0.16 01 E -0.6

A: To find out the correct answer.

Q: Given the lim f(x) = 7 and lim g(x) = 11, what is lim[Ự(*)•g(x}}? %3D г. 28 b. 44 C. 77 If lim f(x)…

A: we know that limit get multiplied when we apply to limit to multiplication of two functions ,…

Q: What does the limit notation lim f(x) = L mean? Xa"

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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: If ƒ(1) = 5, must limxS1 ƒ(x) exist? If it does, then must limxS1 ƒ(x) = 5? Can we conclude anything…

A: A function f(x) is said to be continuous at a point x = a, in its domain if the following three…

Q: Explain what it means to say that lim f(x) = 9 and lim f(x) = 8. As x approaches 4 from the right,…

A: topic - limits

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

A: solution is given below..

Q: Evaluate the limit numerically: lim x → 3 f ( x ), where f ( x ) = { x 2 − 4 x + 2 x < 3 − x 2 + 8 x…

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Q: Explain what it means to say that lim_ f(x) = 4 and lim f(x) = 6. X-2- x → 2+ O As x approaches 2…

A: We have to explain limit

Q: If f (x) = −x + 8 for x ≤0 and f (x) = 4x + 7 for x > 0, find (a) limx→0+ f (x) (b) limx→0− f (x)

A: We can find the limit as below.

Q: Determine whether the following statements are true and give an explanation or counterexample. x-2 1…

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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: Explain what it means to say that lim_ f(x) = 4 and lim f(x) = 1. x- 2* O As x approaches 2, f(x)…

A: For the given limits

Q: What is lim x-->2 f(x)

A: Here we will see the graph and answer as per that....

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 lim as x approaches infinity where

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Q: For f(x) = −x^3 + 1/2x + 8 evaluate limx→∞ f(x) and limx→−∞ f(x). Then give the horizontal asymptote…

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Q: Consider a function x-1 if x 1 (a) Find lim f (x) if it exists. If it doesn't exist, explain why.…

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Q: Explain what it means to say that lim f(x) = 3 and lim f(x) = 8. x-9- O As x approaches 9, f(x)…

A: topic - limits

Q: Explain what it means to say that lim f(x) = 5 and lim f(x) = 1. X-8 As x approaches 8, f(x)…

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Q: Use the e-d definition to show that lim x2 I→2

A: In this question we will use basic of calculus i.e basic of limits. We will simply find the limiting…

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: 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: 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: Find the indicated one-sided limits, if they exist. (If an answer does not exist, enter DNE.) f(x) =…

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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: Suppose that limx→0f(x)=π. Select the best answer below.  3.14<f(x)<π  on some interval  (−δ,δ)…

A: suppose that limx→0 f(x)=π

Q: Explain what it means to say that lim f(x) = 1 and lim f(x) = 4. X- 7- X- 7+ As x approaches 7, f(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: Explain what it means to say that lim f(x) = 9 and lim f(x) = 5. x → 1+ %3D X→ 1 O As x approaches…

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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: Explain what it means to say that lim x → 2− f(x) = 4  and  lim x → 2+ f(x) = 9. As x approaches 2…

A: Given :limx→2-f(x) = 4limx→2+f(x) = 9i.e    left hand limit of f(x) = 4        right hand limit of…

Q: Suppose that g(x) < f(x) < h(x) for all x 2 and suppose that lim g(x) = lim h(x) = -5. Can we…

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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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Q: Assuming that lim x→a f(x)/(x−a)2 exists, find lim x→a f(x)/x-a

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