3 10 Points Use The Definition Of The Limit Or Any Other Tool To Show That The Following Limit Exist What Is The 1 (12.23 KiB) Viewed 31 times
(3) (10 points) Use the definition of the limit (or any other tool) to show that the following limit exist: What is the value of this limit? [sin(n³)]² lim TL Yoon21 2022
= a, ₁b, x₂ = = (6) (Extra credit, 10 points) Let Io = Show that (To+₁)/2 and I₁ = (In 1+In 2)/2. a 26 In - 5 (₁ + ²) + ²/² ( ₁ + (²) 1+ -1)" 2n 3 3 2™ and find the limit: limnoon. [Hint: Look for solutions of the form n =q".]
(7) (Extra credit, 10 points) If {a} is such that a ₁1-ak < Mr for some M > 0 and 0<r< 1, show that this sequence converges. [Hint: Is that a Cauchy's sequence?]
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