Prove that lim n! = 0. Hint: Show that 0 < 2 n! n-2 ≤ 2(3) ¹-² for all n ≤ 2.

Q: 2t2X+ -1 14x2 DAna lim X-7-1 FCx) X-フー1- (-1) 2+21-)) - 2 + 1 ext O And lim 7-1t Lim X-7-1 -1+1 -…

A: Consider the given function,

Q: If || fn-fl|p. os no prove that lim 11 fn V = || f 11 p. له در

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Q: Give a precise €, N argument to prove the existence of 2n +3 lim n→∞o 3n+4

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Q: lim (1,9) >(2,4) || O 12 O 15 09 O does not exist O 6

A: Please refer the attached image for complete solution.

Q: Evaluate the following limit 6n+14 limn0 3n+11 n→∞ 3n+11

A: We  need to evaluate the limitlimn→∞6n+143n+11

Q: Find the following limits. You may use any theorem we have proved, such as Arithmetic of Limits.…

A: Given: limn→∞ 6n2-2n412n3+2n2-17n   Property (i) limn→∞f(x)g(x)=limn→∞ f(x)limn→∞ g(x)    ,…

Q: for Ea, , if lim a,=0 then the root test fails n = 1 Select one: O True 18 O False

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Q: 9" 45. lim n+00 n!

A: Here given as

Q: Show: ( (|fl2 – €)² < lim sup E If (n) < (I|fl2 + e)² , Where ƒ E C(R | Z; , c) n=-N

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Q: nl (n + 1) n" (n + 1)(n+1) nl lim 1, because 0 < < 1. n00 nn 1. OTrue OFalse

A: Solve the following

Q: Let (.) be a sequence of real numbers and let B be the subset of R defined by B :- {A:nEN}. Let i eR…

A: Consider the provided question,

Q: 2 2 - Let S₁ = 3x₁² x₁ + 3x₂² Ax₂ +...+ 3x² Ax, where the Ax;, fill out the x-interval from x = -2…

A: Given that Sn=3x12∆x1+3x22∆x2+...+3xn2∆xn, where the ∆xi fill out the x-interval from x=-2 to x=6…

Q: |x=1| 1 lim x+1 X-1 A True B) False

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Q: 6. a) State why the limit of f(x) = √5x - 1 does not exist for x

A: Please refer to the image below

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A: limN→∞1N∑j=1N19-19jN2

Q: 9n – 5 a) lim n-- 3-n - 18 1 2n2 + 3n – 5 8n? +1 1 b) lim n- o0 || 4

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Q: what is the limit as n goes to infinity of enn! divided by nn?

A: Since e^n &gt; n And rate of convergence (e^n × n!) &gt; rate of convergence (n^n)

Q: 8-x lim - >2 (x-2)(x+1) is O a) -4.

A: In this question, the concept of limit is applied. Limit In mathematics, limits are the points at…

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Q: x² - 4 lim 1-2 +2 O-00 O 4 O 4 O 2

A: Use  a2-b2=(a+b)(a-b)

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…

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A: The objective is to prove the statement: If limsup an=Ln→∞ for a finite real number L and ε&gt;0,…

Q: 10. Prove that if lim(x,) = x and if x > 0, then there exists a natural number M such that x, > 0…

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

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Q: 1 Assume that lim xn +oo. Prove that lim n-00 n +o0. n-00 k=1

A: Given limn→∞xn=+∞

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Q: Compute аn+1 lim n-00 An for (-3)" an = 2n+1 * Enter your answer as a decimal number, not as a…

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

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Q: 3 x-2x-4 limx→2 2x³+3x²-4

A: