65. Is there a number a such that 3x2 ax a + 3 lim +x-2 exists? If so, find the value of a and the value of the limit.

Q: 6- lim メ→2 2-x

A:

Q: /x + 4 – 2 lim x-0

A: Consider the limit, limx→0x+4-2x To estimate the value of the limit, we take some points on the…

Q: Find the limit. x2 - lim x3 -x 3x+2 x-0+ Does not exist 8.

A: This question is based on Limits.

Q: 7. mustrate the definition of the limit by finding values for 8 that corresponds to ɛ = 0.25 for…

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

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Q: lim 1+ 3x = -5 X--2

A: To prove: limx→-21+3x=-5 Solution: Given, limx→-21+3x Here function f(x)=1+3x is a linear function…

Q: т? — Ох — 16 - - Evaluate the limit: lim x →4 x – 4

A: We need to evaluate the limit limx→4x2-0x-16x-4 Which is equivalent limx→4x2-16x-4…

Q: 9. Use the definition of the limit of a function to prove that 4x2 - 7x - 2 lim x - 2

A: The definition of the limit is that the value of the function approaches a particular value with…

Q: Find the limit. 3 lim x-6 5x + 2

A: The given expression is limx→635x+2. We have to find the limit.

Q: Find the one-sided limit

A: To find:limx→-4- x2+2x+4

Q: Use the limit definition to prove that lim n→∞ n-2 = 0.

A: n→∞ n-2 = 0

Q: lim an lim 2 ニ2,

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Q: Q4: Find the following limits if exist:-- x-1 x2-x 1) limx-1²+2x-3 2) limx-1 x²+3-2

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Q: x² – 1 lim x→1 x – 1

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Q: Calculate the limit lim 2√(x-4) / (x-4) As x goes to 4

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Q: 7. For the limit lim (x³ - 3x + 4) = 6 illustrate Definition 2 by finding values of 8 that…

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Q: lim 4x + 3 = 7

A: To provelimx→14x+3=7

Q: 2. Determine the following limits. If the value is infinite, specify o or - o with enough…

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Q: Compute the indicated limits. 5x -3 lim -00 Væ? + 3 5x 3 - lim -00 Vx? + 3

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Q: Use the properties of limits to find the given limit. 12x2 - 7x+9 lim x∞4x +7x-31

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Q: Find the limit. 5) lim /2x + 5 5) x-6

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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: find the limit or show that it does not exist for lim x→−∞ √4x2 + 1 / 2x + 5 .

A: limx→-∞ 4x2+12x+5 = limx→-∞ x4+1x2x2+5x                                =limx→-∞ 4+1x22+5x…

Q: li'n -3Carl) lim -3n-3 ヘ→ 0 ヘう o

A: Yes. It is -3. Just take n common from both numerator and denominator and then put n tends to…

Q: Use the Basic Limit Laws to evaluate:

A: We have to evaluate the following limit: limx→2x3+5x+7

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

A:

Q: 10. Evaluate the limit: -3x -9 x +3 lim x--3+ \x2 +x- 6 x-2/

A: Given: L=limx→-3+-3x-9x2+x-6+x+3x-2 We know that  limx→afx+gx=limx→afx+limx→agx…

Q: 1- Evaluate the following limits, if they exist. If they do not exist, state why. a- Lim 4 c- lim…

A: See the details solution in below

Q: Explain why it is not correct to say but it is true that: (r-l)Xx-2) . Evaluate each of the limits…

A: As in the case of function, since x-2 is common, so there is a hole at x-2=0=>x=2 . So the graph…

Q: Find the limit if it exist.

A:

Q: Find the right- or left-hand limit ớr state that it does not exist. x-4 lim Tx - 4| X-4- Does not…

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Q: Find the limit. x2 - 8x + 15 x3 - 9x lim - 00 O 15 Does not exist 8

A: First factor the denominator and use limit of two sided limit approach,

Q: 2 Find the limit or show that it does not exist. 8. lim (/4x2 + 3x + 2x) X→-0

A:

Q: Find the limit, if it exists. x2 – 1 8) lim X --1 x2 - 6x + 5

A:

Q: Find the limit L. 2x2 + 8x + 6 lim X--3 x + 3 L =

A: Factorise 2x2+8x+6 2x2+8x+6=2x2+6x+2x+6                     =2x(x+3)+2(x+3)…

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: Evaluate the limit 5 + 2x lim 8 – 8x x → 0

A: We haven the function is: f(x) = (5 + 2x)/(8 - 8x)  Dividing the numerator and the denominator by x…

Q: Find the limit. x² - 25 lim x 5 x²8x + 15

A: We need to find the limit:limx→5x2-25x2-8x+25

Q: x² + 9 – 3 lim x²

A:

Q: | | lim 10 - x 10 - x X - 10

A: Now left hand limit is, and right hand limit is,

Q: Evaluate the limit below. - 2x2 + 13x – 21 lim x→3 х — 3 -

A: limx→3-2x2+13x-21x-3apply L hospital rulelimx→3-2(2)x+131limx→3-4x+13

Q: Find the. limit lim 11+X -3 X-2 X+2

A: Given:         limx→−211+x−3x+2

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

A:

Q: Find the limit or show it does not exist. 1- x2 х3 — х +1 16. lim -

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Q: Find the limit. -重班 4x + 4 x² + 2x lim x-2+ Does not exist 4 O- 1

A: Find the limit

Q: Find the limit. lim (2 – x)6 tan(5) |

A: Explanation of the answer is as follows

Q: Find the limit. 7) x6- (x - 6)2 lim A) -- B) = C) 0 D) -1

A: here option b is true

Q: 2. Find the limit algebraically by factoring the expression first. lim x-10

A:

Q: find the limit if it exists at infinity lim=5x^2+7x-9/-6x^2+2

A: Given, limx→∞5x2+7x-9-6x2+2