Discuss the existence of the following limit and state your reasons in this discussion explicitly. e2 (x-1) "(a – lim x4 COS

Q: lim 2(2-1)2 z→1 Z-1 O does not exist None of these is equal to 2 is equal to 0 is equal to 1 O O

A: Ans : does not exist

Q: Identify the values of c for which lim f (x) exists. (x², = {8 - 2x, 2 < x < 4 (4, S(x) x 2 4

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Q: Question 4 Evaluate the following limits: V5x + 2x 4.1 lim Va +9-3 4.2 lim-

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Q: x2 – 21. lim 2x - 8 = 6 -

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Q: 2x²+5 x-4 x→∞ 4 x³+4 x²−2 x+14 Limit. lim

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Q: 1) Answer the following questions based on the graphs. Explain your answer for each part. (No other…

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Q: Question 5 Use the &-8 definition of limit to show that: ( a ) lim(3–2x)=-7 x→5 (b) lim x•cos-

A: Epsilon and delta definition.

Q: Example 2: Consider the graphs of the functions f(x) and g(x) given below. Find each of the…

A: a)limx→1f(fx) limx→1f(fx)=flimx→1fx ⇒f(3) =2 limx→1ffx=2

Q: e 3. Find lim x-o et +1 (a) (b) 00 (c) 0 1 (d) (e) Does not exist and has no infinite behavior

A: The given expression is, limx→-∞e-xex+1 Apply the limit -∞ to the given expression to get,…

Q: x2 – k2 4. For lim x→4 x find all the values for the constant k such that the limit exists. 4

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Q: Write your solution on one piece of paper. Use the given/find method discussed in class, show your…

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Q: I. Evaluate the following limits. 1 1 1. lim x→1+ x – 1 er – e - -

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Q: Question V36x²–6 If r(x) = what is lim r(x)? -8x-5 X→-00

A: Substitute x by 1/t and solve the limit.

Q: Suppose that for a function f, f(3) is not defined. Also suppose that lim f(x) = 2 and lim f(x) = 2…

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Q: Can you please answer this question and show all of the steps and say the correct letter

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Q: x2 dx 81 - x2

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Q: Question 4 x3-8 :- If fx)=x-2 If x1. x+1-

A: Given :

Q: lim x-27 √√√x-3 2/3 x³ -9

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Q: x-27 3.1 lim N-3 X౭-9 x²+2x+1 3.2 lim 3x+4 V1+x2 3.3 lim

A: 3.1) limx→3x3-27x2-9 = 33-2732-9= 00 Hence , we will use L hopital's rule limx→af(x)g(x) =…

Q: Give an appropriate answer. Let lim f(x) = 5 and lim g(x) = -1. Find lim [-3f[x) – 2g(x)] 10+ g(x)…

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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.