8. The graph of function f (x) is shown below: a) For what value(s) of x is f(x) undefined? b) At what value(s) of x is the function non-differentiable? c) Evaluate each limit: i) lim_f(x) ii) lim f(x) x--8+ X→-8- iii) lim f (x) iv) lim_f(x) x→10-

Q: Find the one-sided limit (if it exists).

A: Given: The one - sided limit is limx→-1- x+1x4 -1 .

Q: 7ーズ 1. Find lim using a. Table of values f(x) b. Limit rules

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Q: 2. Construct a table of values to investigate 1 if x -1

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Q: Show that the Product Law cannot be used to evaluate the limit

A: Show that the Product Law cannot be used to evaluate the limit

Q: Use formal definitions to prove the limit statements

A: Given: Function  To Prove:  Formal Definition Of Limit:

Q: limに 1 x2-3x+2 X-1 x-1

A: We have to find

Q: Let lim f(x)=4. Use the limit rules to find the limit given below. lim 20 X-5 lim 200-

A:

Q: Find the one-sided limit (if it exists).

A: Given We have to evaluate given one sided integral.

Q: Find the one-sided limit

A: To find:limx→-4- x2+2x+4

Q: Determine the Limit:  Limx->infinity (1/8)x

A: Consider the given problem:

Q: 34. Show that the Product Law cannot be used to evaluate the limit lim (x - ) tan x. xx/2

A:

Q: Evaluate the limit: lim (x - Inx)* x→0+

A: Using limit definition

Q: Calculate lim x-2 x+2 Evaluate the Limit

A:

Q: 1) DRAW THE GRAPH OF A FUNCTION WHERE lim,-af(x) DOES NOT EXIST FOR SOME INTEGER a. EXPLAIN WHY THE…

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Q: Determine the infinite limit. (а) lim (x – 3)5 x→3-

A:

Q: Compute the limits that exist. lim x---2 x/x - 2

A: Explanation: Given that,  limx→2xx-2     Concept Used: If LHL=RHLLim exist.If LHL≠RHLLim doesn't…

Q: What indeterminate form is the lim (x→+∞ ) x 1/x . Evaluate the limit.

A:

Q: Prove the limit. Using the precise definition of a limit. lim x approaches 5 (x2-x-6).

A:

Q: use l’Hôpital’s Rule to evaluate the limit

A:

Q: 2 lim x→1- x²

A: The limit of the function f(x) is obtained as L=limx→a-f(x)L'=limx→a+f(x) Then the limit of the…

Q: use definition of limit to show:   lim    (4x + 1) =13 x->3

A: The definition of limit:

Q: Use the ε- definition of limit to prove...

A: let the value of the ∂ be ∈3 thus the limit limx→2(3x-2)=4 is proved when the expression…

Q: Once you know lim x-->a+ f(x)  and lim x-->a-  ƒ(x) at an interior point of the domain of ƒ,…

A: If we know the right and left-hand limit of a point then we know the limit at that point.

Q: Compute the limits that exist. lim x---0, x2 + 3x/x

A: Given: limx→0x2+3xx

Q: lim x tan 4 x→3

A: find the value of limt  let L= limx→3 x tanπx4

Q: 10. Use the definition of limit to show that a. lim (x² + 4x) = 12, Z-2

A:

Q: Use the &-e definition of a limit to show: lim (3- x) = -2 | x5

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Q: Calculate the limit if it exists: lim x→4 for 5/(x-4)2

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Q: 10. limx- 2x+x- 713

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Q: apply the formal definition of limit to prove that lim (2x + 9) = 11 x -> 1

A: if fx is a function defined in open interval containing c then limx→cfx=L if for every ∈>0 there…

Q: 4. Using the precise definition of a limit, prove lim (2x +8) = 38. x-15

A:

Q: Find the one-sided limit (if it exists).

A: Given :                       f(x) = limx→2- 1x2-43

Q: Sketch the graph of an example of a function fthat satisfies all of the given conditions. lim fx)2,…

A: Following information has been provided in the question,

Q: lim (x³ + 4x² + 4x – 1) = -1, a-2 1 lim - = 1.

A: Given,

Q: Evaluate the limit 1 lim x--3 (x + 3)²

A:

Q: Prove lim 7-x =6 using the ɛ,8 definition (precise definition) of a limit. x2 2

A: Given data:     The given expression for the limit of the function is: .   The given expression for…

Q: Evaluate the limit, if it exists.

A: The given expression is limx→-2x+2x3+8

Q: 6. Without graphing the function on your calculator, find the limit. Use L'Hopital's Rule where…

A: Solution of the problem as follows

Q: Use the formal definition of a limit to show lim (2x + 1) = 5. x+2

A: Given: limx→2 2x+1=5

Q: Find the one-sided limit (if it exists).

A:

Q: 1) Create a table using appropriate values of x (at least 8 values) and use the result to x² -x- 2…

A: We have to create a table using appropriate values of x (at least 8 values) and use the result to…

Q: Evaluate the limit: Lim X--3 (2-√x² +100 x + 3

A:

Q: Evaluate the limit: lim 1-16 x3-8 x2 limit as x – - > 2 x ^ 4 - 16 divided by x^ 3 8

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Q: Use the graph to evaluate the limit. lim lim Find x-(-1) f(x) and X-(-1)+ f(x)

A: Consider the first given limit: This means that when x is approaching to -1 from left side then…

Q: Find the limit or show that the limit does not exist. lim→-0 4x2 + 3x + 2x x→-∞

A: See the details solution in below

Q: 5, evaluate the limit. 2x3-x 5) lim X0 x2+3x-1

A:

Q: Show that a function cannot have two different limits at the same point. That is, if limx-->c…

A: Let f(x) be a function which is defined everywhere in an interval except x=a, then , If for all ,…

Q: 5. Find the limit of lim x* +0-x

A: Topic = Limits

Q: ) Use the definition of limit to verify lim -3x +2 = –10 x→4

A:

Q: Prove lim(3x–10) =-4 using the ɛ, d definition of a limit. 2

A: Recall: ε -δ Definition :Let f be a function defined in a deleted neighbourhood of 'a' . Then a real…