2. Assume that lim så and lim të exist, and tn ≥ sn for all n. Prove that limtë ≥ lim sɲ. (hint: discuss by cases that lim të is −∞ or a real number or ∞).

Q: b For any be R, use definition to prove that lim-=0. n

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Q: Use the definition to prove that lim (x³ + 2x + 1) = 4. x-1

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Q: i. Using Arithmetic of Limits, find limn→∞ 2n / (3n + 5)&nbsp. ii. Working directly from the…

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Q: Using Arithmetic of Limits, find limn→∞ 2n / (3n + 5)&nbsp. ii. Working directly from the definition…

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Q: Show that the following: If r > 1, then lim Vr – 1 = 0.

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Q: 1) @) Prove that lim an= o if lal <1 and a ER 6) show fon any X with Ix) <1, lim nxn=0- that

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Q: Determine the following limits. If the value is infinite, specify or with enough justification for…

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Q: sec x lim sec(3x) X- 2 5х lim In(2+e*) х>о

A: Given:        limx→π2-secxsec3x we know that secx=1cosx         =limx→π2-cos3xcosx

Q: 3. Show that if then lim an n→∞ = lim a3n+2 nx L = L =

A: We can write n = (3n+2) - 1 - 2n/3. As n approaches infinity, 2n/3 approaches infinity as well.…

Q: Find the limit analytically

A: Given, limit function is

Q: lim 0→0 sin 26

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Q: 8. )Prove that lim Vr = 2 using the e-8-definition. Hint: VI – 2 = x- 4 VI + 2 Puouo thot thoro…

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Q: x - 4 8. Prove that lim Vr = 2 using the e-6-definition. Hint: Vr - 2 = %3D VI + 2 4

A: The ∈-δ definition of a limit is: The limit of a function f(x) as x tends to "a"  is L, that is,…

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

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Q: Let

A: We use definition to prove our result.

Q: Suppose that the lim x2 flx)- Which of the follomng State ment cannot be true ?

A: We have to find which of the following statement can't be true.

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: 1) Use the L'Hospital's Rule to evaluate each limit: sinx a) lim 10 C0S) b) lim In (2x+1) 2x+1

A: L-Hospital Rule:If limx→af(x) =limx→ag(x) =0 or ±∞ and g1(x) not equal to zerothen limx→af(x)g(x)=…

Q: 8. Find the following limit. t+1 a) lim < t- +o 3t2 + 2 b) lim (ti- 3j + VE k) t 2

A: The solution is given as

Q: Let un > 0, Vn € N. Also let lim un = μ. Prove that lim (n + 1) Un+1 = μ. n4x 84x

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Q: . Calculate Lim п? +п —п by using your calculus and algebra skills n→0

A: Definition and methods help to find the required limit of the given function. A value is said to be…

Q: 14. 15. Determine the value of the following limit: lim b) 1/2 — a) does not exist x-3 x-3x²-9 State…

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Q: Budek (B) is a hypothetical quantity used to determine the presence of adamantium in exoplanets,…

A: Given that B=limk→∞∑i=1kyixi∆x And the adamantium is 2π(B-1) which is greater than 100. Now the aim…