1² +1 Use the e-N definition to prove that lim = 1. x² + x + 1

Q: 3 find the limit if it exists .If it do esn't exist, explain why. lim 13+x| X-> -3 2(34+X)

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Q: Find lim 1-0 does not exist -1/2 Ο Οι Ο 1/2 O O Ο Ο Ο Ο Ο Ο O O O e* - r -1 Other: Δ

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Q: See pencil for correction of problem

A: First we simplify the expression (x2-2x-8)/(x+2)=(x2-4x+2x-8)/(x+2)…

Q: 5. a) Explain why lim vx-3 does not exist. b) What about lim V(x 3)2 ?

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Q: Evaluate the limit. 2х — 2п lim x-n |x – 1|

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Q: (2 -1) s lim z

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Q: (a) Using only the e,6-definition of limit, prove that 1 lim = 1. x--1 x2 (b) Let n be a fixed…

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Q: lim 1. m, n > 1 is

A: We try to find the limit by substitution

Q: 2n +1 a) Using the definition, show that lim n00 3n +4 3

A: Given,           limn→∞2n+13n+4=23

Q: (a) n+ (-1) 2n lim

A: limn→∞-1nn+12n

Q: lim 21/* is no limit 1

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Q: *+1 Find lim H00 3x - 4x +5 if it exists. Find lim(1 + r), if it exists. X-4

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Q: 19. lim (-1)"+' (") does not exist. n00

A: Given  The limit is limn→∞(-1)n+1n-1n

Q: Evaluate the limit 4 b lim b->4 2- V6

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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: find the limit or explain why it does not exist

A: To find the limit.

Q: Prove that lim š +1) = 3 using the e-8-definition.

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Q: 10* – 5* – 2* +1 (b). Evaluate lim- VI+x-V1-x (i).Evaluate lim- sin-!

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Q: 1- 2x Prove that lim = -1 using the e, d definition of a limit. 5

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Q: lim In(x+3) 4) 1

A: Evaluate :     limx→∞ln3xlnx+3

Q: 4-VE Find the limit: lim→16 x-16

A: We need to evaluate the following limit limx→164-xx-16

Q: 17. If lim- X- 200 – 4n + kn² then k =

A: Given

Q: 1. (f Use "e- N"-statement to prove that lim n 1 [Hint: Ve > 0,3N(e) = > 0, Vn > N, we have n- %3D

A: We have to show that given limit of function converge to 1-

Q: -4 Determine the limit: lim -i (и — 1)2

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Q: 6-2x Prove by definition that lim 4. 3

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Q: 5.6. Prove that: (b). lim z0 Z (а). lim does not exist, = 0. - ||

A: The given problem is to prove and evaluate the following complex variable limits.

Q: 1+n Prove using the definition of the limit that limn→∞ 1-2n 2

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Q: 1. (a) Use the e - 8 definition of a limit to prove lim(7x + 3) = 38. X5 t010-1123.then fex)-LI…

A: Given,

Q: Q \ Find the value of 8 > 0 that guarantee lim x-0 csc(1/x) = 0 in terms of ɛ?

A: Definition of limit: We know that, limx→af(x)=L               ...(i) For each ϵ>0, there exists a…

Q: 2t – 1 Evaluate lim,, tan-1, e> - t - 1

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Q: x² - 225 = 30 Give an ɛ-ô proof of lim X- 15 X→15

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Q: Determine the infinite limit. x² - 4.x lim 1+4+ x2 - 8r + 16

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Q: 10. a.) Use: lim 2(x1 )Ax = ] Ax)dx , i-1 b- a and x; = a +i Ax Ax = to evaluate (5x - 2x³ ]dx. b.)…

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Q: Determine the infinite limit. lim In(x2 – 25) x-5+ 00 -00 8

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Q: Estimate the value of the limit to at least 2 decimal places. 22 - 64 Let lim I→-8 -+ 10x + 16

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Q: (220_ 3.x)– (e20_3e) lim -3x is x-e

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Q: (3) Find the limit. 1- x lim 1+3- X – 3

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Q: 7) Show that lim = 1. 200 (z-i)3

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Q: Prove that lim r = 2 using the e-8-definition. Hint: VI - 2 = VT + 2

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Q: 3n³-4n+1 Find lim,00 . (show all necessary en details)

A: Limits are used to calculate the approaching value of the function at which the exact value of the…

Q: Evaluate the limit: 4(22 - 1) 3x (x – 1) lim |

A: Given : limx->4 4(x2-1)/3x2(x-1)3

Q: 18 -a+1 Find the limit lim a9 2x2+3x-1

A: Given, limx→918x2-x+12x2+3x-1   To evaluate limit

Q: 4. Determine the infinite limit. lim In (x – 2) x-2+

A: Solution is here

Q: 5x 3 lim 1+ Compute the limit: x→

A: We can have a approach for this kind of question in which we get indeterminate  form 1∞

Q: 23 - Vx - 47 Find lim x+ 24 X→-24

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Q: x2 - 144 = 24. 1) Give an e-d proof of lim x- 12 x→12

A: proof of The proof, using delta and epsilon, that a function has a limit will mirror the definition…

Q: Determine the infinite limit: lim (x – 3)5 I-3-

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Q: I - 4 Prove that lim vI = 2 using the e-d-definition. Hint: Va - 2 = VT +2

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