x2 – 21. lim 2x - 8 = 6 -

Q: Using the € - d definition of limit, prove that 2x lim x 2 x + 6 1 NI

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Q: Evaluate each limit, if it exists: x²-4 a)lim 22-4 X-2 1-x² b)lim x-1 1-x x²-4x x-0 x(x-1) c) lim

A: Here we have to find the limit of the functions.

Q: Using the formal definition of limits, show that lim (-2x + 5) =-1.

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Q: Evaluate each limit, if it exists: a)lim ²-4 X-2

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Q: find the limit or explain why it does not exist

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Q: Indicate a type of an Indeterminate Form, and find the limit. e 10 Limu0

A: diven:limu→∞eu10u3

Q: 6) lim X-0 x3 - 6x +8 X-2 A) -4 B) 4 piecewise function is given. Iso the mu C) 0 D) does not exist

A: limx→0x3-6x+8x-2

Q: ° (24 -2x + 2) I-4

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Q: I need to compute each limit. I have attached the problem as a photo.

A: Given:

Q: 4n + (-1)" 4n +n existence of this limit using the definition in terms of e and N(c). State and…

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Q: Find the limit, if it exists. If it does not, enter "DNE" (2a + 2)(x - 5) lim 22 +2

A: Given limit is in the indeterminate form, just use the L'Hospital's rule and easily find the…

Q: explain the purpose of a proof by ε, δ definition of a limit.

A: Here I give the geometrical view of definition.

Q: Question: In what ways might the limit not exist? Describe in words and demonstrate with graphs. 4.

A: To describe: the ways the limit not exist.   Limits fail to exist for one of four reasons: 1. The…

Q: can you find the limit, and if it doesn't exist can you put DNE

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Q: n! - (n+ 1)" lím (1+m) · (2+ m) ·. .· (n+ m)

A: Given expression is    limn→∞n!n+1m1+m2+m...n+m We have to find limit when m=2 and m=3.

Q: lim et 2x3+x2 +3x-4

A: Solution of given problem is followed by

Q: 4 + 9x ≤ f(x) ≤ 12 + x²

A:

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…