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

Q: Evaluate the limit using the Basic Limit Laws

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Q: 6- lim メ→2 2-x

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Q: limX 7+ メーマo

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Q: Find the limit (if it exists). If it does not exist, explain why.

A: first we factor the denominator

Q: Evaluate the limit. 1 1 lim x--4X + 4

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Q: Use continuity to evaluate the limit. ,2 lim 2x - 4 X→4

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Q: x2 + 8x – 9 4. lim x→1 x3 2а? — 5х + 6 - -

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Q: Evaluate the limit: lim 5x 6x %3D

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Q: (x²–4) lim x→-2 (x+2)

A: Given: Let y=limx→-2x2-4x+2 To Find: To evaluate the given limit.

Q: Using the ε−δ− definition of limit, show that limx→3(3x−2)=7.

A: Given:

Q: lim an lim 2 ニ2,

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Q: x2 – 21. lim 2x - 8 = 6 -

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Q: Evaluate the limit using the appropriate properties of limits. 4x2 - 7 lim 3x + x - 3

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Q: Use the definition of limit to prove lim {x -> 5} = 2x-3=7

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Q: Evaluate the limit using the appropriate properties of limits. 9x — х + 5 lim х > о 7x? + 5х — 9

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Q: lim +2 2 7²-1 €³-76 +9 2

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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: Compute the limits that exist. lim x---8, x2 + 64/x - 8

A: The limit of a function limx→Xf(x)=Y means that value of  function fx can be as close to Y by making…

Q: prove the statement using the δ definition of a limit. | such that if 0 0, we need δ i-Select…

A: For given epsllon>0, we choose delta=5epsilon/2 .Tnen By definition of limit, we have limit of(…

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: compute the limit (or state that it does not exist) assuming that lim n→∞ an = 2

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Q: lim 4x + 3 = 7

A: To provelimx→14x+3=7

Q: Prove the statement using the &, & definition of a limit. lim (1 – 4x) = 9 X- -2 !!

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Q: Use the definfition of a limit to shoe that limx->3 (5x+9)/(3x-1) = 3

A: Recall: Definition of limit : Let f be a function defined in a deleted neighbourhood of a. Then a…

Q: Evaluate the limit. 6. lim xtan

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Q: Evaluate the limit using the Basic Limit Laws

A: To find the limit  limx→5x-2

Q: By using the e –- N definition of limits, prove пз — Зп - = 1. lim п00 п3 — п — 2

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Q: a) Prove the statement lim +3 by using the ɛ, ô definition of the limit x→6 4

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Q: Use the precise definition of a limit to prove the statement: = 2 -, (2x)

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Q: Prove the statement using the ε, ?  definition of a limit.

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Q: Evaluate the limit using the appropriate properties of limits. 6x2 - x + 5 lim 4x2 + 5x - 2

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Q: Use the ε, δ limit definition to prove- lim x→-1 (3x-5) = -8

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Q: Compute the limits that exist. lim x----5 2x2 - 5x - 36/8 - 3x

A: To compute the limit: limx→52x2-5x-368-3x Solution: Evaluating the limit.…

Q: Evaluate the limit. lim (4x)/

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Q: Determine the lim 2x - 2x2 - O-2 The limit does not exist

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Q: lim r² = ∞ 1418

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Q: Prove the statement using the ε, δ definition of a limit. limx→3 (4x − 5) = 7

A: To solve the given problem. limx→3 (4x − 5) = 7

Q: – 32 x3 + 6x? – 32 lim x--4 x3 + 5x2 + 4x

A: we got 0/0 so we apply L'Hopitals rule Take derivative of top and bottom by applying power rule

Q: 8х + 15 - Evaluate the limit: lim х — 3

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Q: Using the ε−δ− definition of limit, show that limx→2x2=4.

A: to find the limit limx→2x2=4 proceed as follows using the definition of limits there exists δ>0…

Q: 4. Use left and right hand limits to determine if the following limit exists, 22 + 2x - 3 lim 2-3

A: To find:- Use left and right hand limits to determine if the following limit exists

Q: Use formal definitions to prove the limit statements

A: Given: limx→-5 1(x+5)2 = ∞ To prove: The limits using the formal definition.

Q: 19. lim 1– 3 = -2 3. 20. lim = 7 2 x- 2)

A: ε-δ definition of limit: Let f be a function defined on an open interval I. Let x0∈I. Then the limit…

Q: By using the definition of limit, prove that limx→-3 2x+9 II

A: solution is given below..

Q: x² + 9 – 3 lim x²

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Q: Evaluate the limit lim x²sin 4x2

A: We can use substitution In order to solve this problem.

Q: 6x+5x-1 lim X--1 7x-2

A: Topic = Limits

Q: Evaluate the limit using the appropriate properties of limits. 7x2 – x + 6 lim X - c0 4x2 + 5x - 4

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Q: Evaluate the limit: lim 4у — 3 %3D y→ - 2

A: Consider the given expression is, limy→-24y-3

Q: Evaluate the limit lim Va x + 3x + 11 – x 2 -

A: