The authors explain the following limit property in terms of APOS. limx → afx + limx → ag(x) =limx → a(f+g)(x) Calculus students often make mistakes in applying this as well as other properties of the limit. For example, I have seen students who have had difficulties in understanding the following property: limx → ak*fx=k* limx → af(x) What do you think is the reason of students’ difficulties with these properties?

Q: Sx² – 4 if r 3 (a) lim f(r) - (b) lim f(x) = (c) lim f(r) = 3-

A: see 2nd step

Q: If the fucntion f is undefined at x then lim f(x) does not exist. = c, C, FALSE O TRUE

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A: Given query is to find indicated limit.

Q: O 8: Evaluate limits of functions from their graphs and/or equations. Find lim f(x), lim f(x), lim…

A: Given, Graph  of the function:

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Q: Let limx→a f(x) = ϕ and limx→a g(x) = γ. Then the following statements apply: a. limx→a (f(x) +…

A: Limits describe the behavior of functions as their inputs approach a certain value.The theorem…

Q: Evaluate each of the following limits: (a) lim (2+³) (b) lim (2t-³) t→∞ ∞047 (c) lim (2+³) t→0+

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Q: Explain why you cannot use the substitution to determinate the limit lim(x->inf)(|x|/x)  Does the…

A: Substitution means we directly substitute the value of x in the function.

Q: Consider the function f(x) = {,* - a, -1<x< 2 lb – 2x, 2<x<4 If b =1 and the limit of f (æ) as æ → 2…

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Q: 3. Find the indicated limits. if x 2 f(x) -2+ 4x – x² a) lim f(x) x→2+ b) lim f(x) x→2- c) lim f…

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Q: Find the limit of lim, 1 f (x) if f (x) = 3 - x, if x +1 and f (x) = 1, if x = 1

A: For the  given statement

Q: Take f, a and ϕ as in theorem. Show with the calculation rules that: a. for every k ∈ R holds limx→a…

A: Let lim x→a f(x) = ϕ and lim x→a g(x) = γ. Then the following statements apply:a. lim x→a(f(x) +…

Q: Find the following limits if they exist. Must show all work (analytically?): 1. X-2 lim (x) where…

A: Given that: 1. limx→-2f(x), where f(x)=-3x2+8, if x&lt;22x,          if x&gt;-2   NOTE: As per our…

Q: if x1 then lim,-1 f(x) is 3 if x 1 (b) 3 3. Let f(x) = (a) 1 (c) not exist (d) other

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Q: 5. Calculate lim f(x), where x+1+ f(x) = = its 12.05 (c)-2 (d) 2 (e) does not exist 5A 5B if x 1 x-1…

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Q: Choose the best answer for limit.

A: Given, limx→4- fx=limx→4+ fx=5

Q: (a) 1? - 9 lim --3 21? + 7t + 3 (ांच 1 (b) lim t/1 + t 4 lim x--4 4 +E x (c)

A: Since you have posted multipart questions i can do first three subparts as per our company…

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Q: 3e -2 Find exact values for the following limits (if they exist). To get full credit you must…

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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.