Let A, = [n,n+ 1] and B, = [0,3+ [ for all n eN. 1. HL lim 42(A,) 2. PL B =2 MEN 3. PL An lim pz(A,) 4. PL B. = 3. NEN 1

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

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Q: . Determine lim 818 ax ( 2² + a² + b) ª 3 r² where a, b and c are nonzero constants. I mazá $…

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Q: 1) a)lim n(a (aa – 1) =?

A: Given: limn→∞na1n-1 We can write, limn→∞na1n-1=limn→∞ a1n-11n We get the indeterminate form

Q: lim z+di = 1 Z-1-21 I lim 2 Z-0 lim 240 (Im²) ² 12₁²2² does. (Rez) --121 - compute 0 lim 7731 Z 27²…

A: We will find the required.

Q: need the answer as soon as possible

A: Sequence convergess to 0

Q: 1. If lim an = a then lim an+10 lim an–10 = a. n-00

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Q: 84. Prove that if lim ar = L, then lim ak11 = L. k00 %3D k00

A: limk→∞ak=L

Q: Evaluate I (n +) lim as n → 0 Vn[ (n + 1)

A: We have to evaluate limn+32n⋅n+1 as n→∞ that is limn→∞n+32n⋅n+1 We know that n=n−1! Hence,…

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Q: 4. lim ) ズ→1 Xー1

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Q: 3. [32] −1 4-3 4. 5. [. |_3 -4 2 1 2 -1 4,

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Q: Fird the vaue al lim 3. 1-3 (al 18 (b) 10 (e) 1/12 (d) -10 (e) -19

A: To find the limit we have to put the value of x in the given expression. If the expression give…

Q: Evaluate N εν Σ √19 lim N→∞ N 19 19 19(1) - 2

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: Determine which of the álfewng, segrences ar. monotonic Then gques their fimits Cwhere applicatole)…

A: In calculus ,a function {\displaystyle f} defined on a subset of the real numbers with real values…

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…

Q: 4. If tige Lim, show that fg & LUM.

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Q: O 2x-12 fix)<x? for OLx3, Find lim flIN) <ーフ」

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Q: 2n j3 lim - 24n n00 j=1

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Q: 2. Let r > 1. Prove that lim r" = 00,

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Q: 7x + 6 17) lim V6x2 + 1 X-00

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Q: Find the limit 19sin(5x) lim 28x x-0 a. 5 28 Ob. 95 28 19 О с 28 d. None of these. O e. 95 28

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Q: Determine the limit 2x z 3 lim,> 3z2 1 8x |5 O x=2/3 O x=-5/2 O x=-2/3 O None of the Above

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Q: Q4) Prove each of the following: V12-- 1- Prove that lim -7 3 VO-3 2-If y - (tan3x)" prove that -…

A: Given: 1) limx→3(12-x-x6+x-3)=-7 2) y=(tan3x)2x, dydx=(tan3x)2x(6xsec23xtan 3x+2ln(tan3x))…

Q: 2) (9modoxT) I J16T I MAXI x2 a). Show that if |x +3|< 1, then 72√x +31. mod 2. Consider lim 2113 2…

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Q: Evaluate the following linits ) lim lim cos mn Cos nx

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Q: 5. Let x X for n-1,2,3,.... Then lim "n+ n- X n" n A) e B) e2 C) e D) e E) 1

A: First we plug expressions for x_(n+1) and x_n in the given limit.

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: 1+ V5 Let s1 = 1 and for n > 1, let sn+1 = Vsn +1. Show that lim s, = 2 n00

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Q: i. Find the limit of the following. 4n -2n + 4n 2n +7 n+4 n – 5n+6 a) lim n - 2n 5n -3n b) lim -16…

A: We have to find the limit of   e) limn→0nensin n f) limn→32ln(4n-11)n2-9

Q: Find: L . -im Z÷1+1 L Z²+1 2 Z²_1 im Z10 +1 7/0 14-Z 6 Z+1

A: (a). The given limit is: limz→1+iz2+1z2-1

Q: Compute the exist i. lim 8+iz 2--2i z+4 following limies if they . ¡i. Gm Rez.

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Q: 11. If 0 < a < b, determine lim Qケ+! a" + b"

A: First we take comman bn+1  from numerator and bn  from denominator and then we  use lim ban=0.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.