Which of the following is/are signified by lim f(x) = 0? O The limit exists and equals infinity. This means that f(a) = ∞ |As x approaches a, the value of f(x) increases without bound. O The value of f(æ) becomes infinite when a approaches a. O The value of x goes out to infinity, when it gets close to a.

Q: B. Calculate each of the following limits, or explain why it does not converge. i. lim, - 1 (x-2) /…

A: We have given limit, we have to find the value of limit.

Q: lim x* +x

A: Given,          limx→01x-1x2+x

Q: 32 Evaluate the limit, if it exists. (x + h)³ – x lim 3 h

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Q: tan x lim 4-V lim x-16 16x-x² x² -9 lim x-3 x²+2x-3

A: Find the value of limit limx→πtanxx. limx→πtanxx=tanππ             =0π            =0 Thus, the value…

Q: Find the limit, if it exists: X lim X+- 0 x² + 1 ,2

A: We factor out x2 from inside the square root. Then |x| comes out of the square root. Note that: x/…

Q: Use a graph to investigate lim f(x) at the number c. (If an answer does not exist, enter DNE.) S3x…

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Q: 10. Let a be a positive constant. Evaluate lim x(a/x – 1) if the limit exists. If the limit does not…

A: limx→af(x) does not exist. The idea is that there is no number that f(x) gets arbitrarily close to…

Q: 10. Find the value of the limit or state that it does not exist b) lim f (x) =

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Q: 6. Use the graph of the function f(x) = He to discuss the limit lim 40 f (x). 1+e!/x

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Q: Compute the following limit if it exists. x? - 5x - 36 lim x- 9 X-9 Select the correct choice below…

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Q: 1. Let f(x) = 5, if x>1 f(x) = 2, if x < 1 f(x) = undefined for x = 1 Find the following one sided…

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Q: Using the precise definition of a limit, à in terms of & for lim (2-3x) = -4 is E/-3 X-2 A) True B…

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Q: D-the result of the following limit is 1² lim x-0 In (sec x)

A: Let's evaluate given limit.

Q: 1 Discuss the existence of the limit lim x 0 x2"

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Q: Find the limit. lim X-2 x+2 O 1/2 -00 O Does not exist

A: Answer is limit does not exist

Q: Consider lim e-. a) lim 4x - x² = 0 b) If we let t = 4x - , then we can rewrite the limit as lim of

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Q: 7. Find the limit, if it exist x² +2 a. lim xV9 - x? C. im b. lim * x-1

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Q: If the limit does not exist, say why. (If the limit does exist, so state.) -The limit does not exist…

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Q: Suppose that f(x) 0 for all a in the interval (-1,1). If lim f(x) = L, then %3D L> 0. For those who…

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Q: Please

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Q: 1. Evaluate the following limit: x? -4 a. lim- 1+2x + 2x – 8 (x²-9) 2 b. lim 1+3 (x -3) (t - 3) c.…

A: If putting the value of variable value of function approaches 0/0 we should apply L hospital rule…

Q: When proving the limit lim(x² + 4x - 1) = 11, and e > 0 is given, what is an appropriate choice for…

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Q: Only one of these calculations is correct to evaluate the limit lim xe ex? Select one: xe-x? = lim…

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Q: Evaluate the following limit. lim /x + 13 x-6 Select the correct choice below and, if necessary,…

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Q: 3].. Use € Use e – 8 definition of a limit of function to show that: 2x = 1. x→1 1 + x a) lim X- b)…

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Q: Find a value of the constant k such that the indicated limit exists. 8 -5 lim x-0 ekx +5

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Q: Evaluate the following limit. (If the quantity diverges, enter DIVERGES.) lim (-1)" (7n – 1) 5n + 1…

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Q: 2. Given lim= 2, X-2 X Use the precise definition of a limit to find the values of 8 that correspond…

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Q: 2. Calculate the limit algebraically. x-11 lim O -1.8 03 -0.6 O 1.8

A: Given

Q: 1 Find the limit: lim X-I x+1

A: Our Aim is to find limx→(-1)-1x+1 -(i)

Q: Consider the following. 2 + 1 if x * 1 f(x) = if x = 1 X -2 -1 Use the graph to find the limit below…

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Q: 2. Determine the following limit. 450 lim x→∞ 9+3 .1.2-0.25x+10

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Q: Q5. Find the value of the limit: lim (z - in

A: See the attachment

Q: The question asks to, "evaluate the limit using an appropriate substitution."

A: Calculation:

Q: Find the following limit: lim f(x) X-3 O A. 0 В. 1 O C. -3 O D. The limit does not exist

A: Let's find the following limit.

Q: x" -1 :? x+1Vx -1 For a positive number nEN, what is the value of the limit lim-

A: On substituting x=1 in limx→1 xn-1x-1 tends to 00 (Indeterminate) form So upon applying L-Hospital…

Q: Consider the following. -2 ifx -1 if x = -1 fix) = -2 y -2 -1 <-1 -3 Use the graph to find the limit…

A: We need to find limit at x→-1.

Q: If n is any positive integer, then the limit lim x→0+ xn ,what is the limit? O +00 Indeterminate

A: Given: Let y=limx→0+1xn, Where n is any positive integer. To Find: To evaluate the given limit.

Q: What is the value of a, such that after Inx+x direct substitution the limit lim gives e ax Select…

A: We have to find the value of a . I have explained in details please see the explanation and if any…

Q: Find the following limit: lim f(x) X-1+ O A. -1 Ов. 1 ОС. 3 O D. The limit does not exist

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Q: 3 (а+h)2-За? Algebraically calculate the exact limit: lim h→0 h

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Q: 1 Find the limit of lim x (1– e * ). X→ 00

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Q: 45. Suppose x. ifx 1/n for every natural number n, f(x) ={0. otherwise. b) Does lim, 0f(x) exist? If…

A: Given :f(x)=xx=1n ∀n∈ℕ0otherwiseTo check :limx→0f(x) exists?Formula :By Archemedian property ε&gt;0…

Q: 1. Give an example of a function g for which lim g(x) does not exist, but the function I+2021 value…

A: We have to find the required example first.

Q: 44. Prove that if lim f(x)= L #0 and lim g(x)= 0, then the limit lim 8(x) does not exist.

A: Given: limx→cf(x)=L≠0 and limx→cg(x)=0 To Show- limx→cf(x)g(x) doesnot exist. Theorem- if limx→au(x)…

Q: Q1 find the limit x' -1 lim x –1

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Q: By definition of limit , find o from the following * lim (-3x – 2) =1 e = 0.03 x→-1

A: Since you have asked multiple questions, we will solve first question for you. If you want other…

Q: Given that lim,+ f(x) = 3,lim,++0 9(x) = -5,lim→+0 h(x) = 0. Find the following limit,if it does…

A: • If the limit is finite and unique, we say that the limit exists.

Q: What exactly does lim

A: Definition of the limit: Consider f(x) be any function that is defined on the the open interval…