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: Let a,=l.cayider the sequeue fany generated It anti= an (a) Shaw that Lim an= Ø ,where Ø= !t v5 x…

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Q: Find а) b) a? - an ww. lim lim x→a I – a

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Q: Suppose that lim an = 5 and lim bn = 9. n-0 n→∞ Determine the limits. lim (an + bn) = n→∞o lim a =…

A: We are given that limn→∞an=5 and limn→∞bn=9.We need to find the given limits.

Q: Assume lim,→a f (x) = L. If f(x) > k, prove that L > k. Prove by con- tradiction by assuming L < k…

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

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Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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Q: lim 0→0 sin 26

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

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Q: Let

A: We use definition to prove our result.

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Q: Show that the limno (1 + )" exists in a detailed proof, and find the limit.

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Q: Assume that lim sn = s and sn>0. Prove that s > 0.

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