Suppose that {a} and {b} are two sequences of real numbers, and that a → L and n=1 n=1 → L where L & R and L = ± co Let {c} be the 'interlaced' sequence a, b, a, b,... defined by C2m-1 = m² 2m = m a b n=1 Use the definition of limit to show lim c = L. 11 → 00

Q: Let x₁ = 5 and x n+1 = X n 2+4 2x n n 1. Find lim x " n n→ ∞

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Q: Find the limits

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Q: 4) Evaluate the following limit: А — 16 lim x→2 - (x – 2)²

A: Consider the limit

Q: Using the precise definition of a limit, à in terms of & for lim (2-3x) = -4 is E/-3 X-2 A) True B…

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Q: 5. Prove the following using the e d definition of a limit: lim 3 − x = −5 r-10

A: The given limit is limx→103-45x=-5 we have to prove the limit using ε-δ definition of limit.

Q: Evaluate the limit sin 2x 6m lim 10

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Q: Compute the limit lim Ssin n2 .1+n2 (규)]. n00

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Q: Use the e-d definition of a limit to find a 8 > 0 for arbitrary e > 0, for lim (4x 3) = -27 (Use…

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Q: 5. Rationalize the numerator to evaluate the limit. Be sure to show all your √³+49-7 h³ Q(²) = 0 lim…

A: First of all we will rationalize the numerator then we will apply the limits

Q: (b) lim (r + 1) In x

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Q: Evaluat the limit si a. lim (Itx)"-1-nx ー1-nx x2 メ

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