Suppose that (sn) and (tn) are sequences so that sn = tn except for finitely many values of n. Using the definition of limit, explain why if limn → ∞ sn = s, then also limn → ∞ tn = s.

Q: х?-2х-15 lim х>5 х2-6х+5

A:

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

A:

Q: Evaluate the limit. 1² – 4x + 3 lim 3x3 21 +3

A: To evaluate the limit limx→∞x2-4x+33x3-2x+3

Q: 1) Find the Limit lim/→0 3x²h-7th+h h

A:

Q: 3n²+ 2n 32 (a) n² - 11 (b) (7) Hint: 4" = (2¹)²

A:

Q: Prove the limit statement using epsilon-delta 3x2 - 8x-3 x -3 2) lim x-3 = 10

A:

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

A: Consider the limit

Q: 1 z+1-4 lim Z→3 Z-3

A:

Q: Find the limit

A:

Q: Calculate the following limit(s) if they exist. x3 7) lim x3-1 Enter just an integer or a fraction.…

A:

Q: These are alternative definitions of the limit of sequences. Can you please help identify what is…

A: Given: limn→∞an=a if ∀ε>0∃N∈ℕ such that ∀n≥N  an-a3<ε To Find: Identify what is wrong with the…

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

A:

Q: Using each time the appropriate definition of limit, determine the following limits. (Observe that…

A:

Q: Suppose that (sn) and (tn) are sequences so that sn = tn except for finitely many values of n. Using…

A: Every finite set A of natural numbers has maximum and minimum numbers.

Q: Evaluate the limit.

A: Given:                     limx→∞e4x-1-4xx2 Dividing the numerator by highest power denominator:…

Q: eax lim x → 0 In(1+ bx) -ах e

A:

Q: an + an-1 An+1 Vn +1 (a) Find the limit of an as n → ∞ and give a proof. converges for a,n from part…

A: Given, an+1=an+an-1n+1 the sequence is all positive number. (a) we need to find the limit of an as…

Q: х2—1 lim х-1+ In(x)

A:

Q: Specify the string limit value:  lim n-->oo  n(3ln n - ln (n2 +1) - ln (n-1))

A: L'Hospital rule: limx→cf(x)g(x)=limx→cf'(x)g'(x) Quotient rule of differentiation: fg'=gf'-fg'g2…

Q: . Find two sequences {an}o and {b»}_o such that lim 0o. As part of your solution, explain…

A:

Q: Using the e - N definition of a limit, prove that 8n lim n+00 4 = 2 4n – 1 -

A:

Q: In(9x) (d) lim x2

A:

Q: Explain why if an converges, then limn→∞ an = limn→∞ an+1 . I need explanation why this theorem…

A:

Q: □ O 5 16 0_5 4 4n²5n+6 no 5n²+ 4n+7' 27. Evaluate the limit of lim

A:

Q: Let an 2n+4n-3 Using the definition of the limit, prove that lim,∞ an 3n2+2n+1* 2/3.

A: Given that, the rational function  an = 2n2+4n-33n2+2n+1 To prove that limit of function is limn→∞…

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

A:

Q: x" -1 :? x+1Vx -1 For a positive number nEN, what is the value of the limit lim-

A: On substituting x=1 in limx→1 xn-1x-1 tends to 00 (Indeterminate) form So upon applying L-Hospital…

Q: lim x* + 5x2 – 12x + 3 x→-2

A: Given function is: limx→-2x4+5x2-12x+3

Q: Suppose {Pi} and {qi} are sequences of real numbers such that lim pn = p and lim qn = q. Give an e-N…

A: suppose pi and qi are sequences of real numbers such that   limn→∞pn=p  and limn→∞qn=qSo by…

Q: Find the limit

A: It is given that,limx→2x2+2x-8x2-x-2We have to find the limit.

Q: (2n+1)!+(2n+2)! )! (2n+3 lim

A:

Q: Find the limit

A: