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→ ∞

A:

Q: Find the limits

A:

Q: 3. Let f : R - {0} → R be such that the sequence (xnf (xn)) converges to 3 whenever (xn) is a…

A:

Q: 2.2 a) Prove that lim,-2(x +2x – 7) = 1 using the e- ô definition of a limit. b) Find lim,-2 arccos…

A:

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

A: Consider the limit

Q: Find the limits lim(2 - 3 as 1/3 a. t→0* b. t-0

A: Given function is: ft=2-3t13 As t→0+ we get, limt→0+ft=limt→0+2-3t13=2-∞=-∞

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

A:

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…

A:

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: S* 56sin(t")dt Evaluate the limit lim .8

A:

Q: 2. Find the limit of the following functions C. x-5 lim x-5x225,

A: here we have to find the limit of a function.

Q: 2. Find the limit of the following functions f. lim x →∞0 x5 - 3x + 1 x-5

A: The given limit is: limx→∞x5-3x+1x-5

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

A:

Q: 91. Prove the second part of Theorem 1.31(a): If k > 0, then lim x-* = 0. x00

A: Write x-k as 1xk to get limx→∞1xk. Plugin the limit to get 1∞k.  limx→∞x-k=limx→∞1xk=1∞k

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

A:

Q: Va – V22 lim x → 22 х — 22 - (Use

A:

Q: lim, (1 + -)* O 0 .0, 1°, 1°, 00-0, 808 40, 1, 1°, 00 - 0, 9

A:

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

A:

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: EVALUATE THE LIMIT OF THE GIVEN FUNCTIONS

A: Given, To find limx→∞ x42x-12

Q: Every limit as x → o can be expressed alternatively as a one-sided limit as t → 0*, where t = x-1.…

A: Given- limx→∞3x2-x2x2+5=limt→0+3-t2+5t2 To Prove- The above value of the limit using the quotient…

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

A:

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

A:

Q: Find the limit

A: