The limit is a right-hand or left-hand Riemann sum Σ f(t;)Δt. For t; = πί/n, write the limit as a definite integral. n-1 lim Σ 5 cos( i=0 πίπ n k/? n

Q: Determine the monotonicity and boundedness of the following sequence 4" 2n + 100 an=

A: Determine the monotonicity and boundedness of the following sequence a_{n} = (4 ^ n)/(2 ^ n + 100)

Q: For each sequence {an}1, prove it converges by showing that it is bounded and mono- tone, and find…

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Q: miformely cari formely Show that Sum of two is Conuergent Convergent. sequence

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Q: Determine the limit of the sequence a, (-1)* 1 1 2 2 - 1 Divergent

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Q: Find the limit of the sequences with general term as given: (e) (√4 - √1/n  - 2)n (f) (-1)n √n / n…

A: Answer

Q: Show that the sequence defined by 1 a₁ = 1 an is increasing and an < 3 for all n. Deduce that {an}…

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Q: Use the given graph of f to find the Riemann sum with 3 subintervals. Take the sample points to be…

A: The interval, [0, 6] Number of subintervals, n = 3. a = 0b = 6∆x = b - an = 6 - 03 = 2 The x -…

Q: Exercise 5. Prove that a non-decreasing (resp. non-increasing) sequence which is not bounded above…

A: Let an be a non decreasing sequence . ⇒an&lt;an+1  ∀n∈ℕ Since an is not bounded above so for any…

Q: , Find the limit of this sequence, or else prove that the sequence diverges: (1- 3 In n an =

A: ANSWER

Q: If ( a n) is a sequence that diverges to ∞, prove that Iim n --> ∞ (1/a n) = 0

A: Assume that the sequence an diverges to ∞. That implies, limn→∞an=∞.

Q: Find the first four terms and the nth term of the sequence of partial sums associated with the…

A: 1, 2, 3, 4, ......, n, ....... Now first partial sum is, S1=1 Second partial sum is, S2=1+2=3 Third…

Q: For the sequence {a ,} if a,→ L, and f(x) is a function defined at all a, then f(a ,)→ f(L) Select…

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Q: (n + 1)! Determine the limit of the sequence a, n! 3 1 2 1 1

A: find limit of sequence

Q: Assume that the following sequence has a limit L. Find the value of L. 41/3, (4(4/3))\/3,…

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Q: Let (2) be a bounded sequence. Prove that if (en) is monotonically decreasing then it con- verges to…

A: To prove that a bounded, monotonically decreasing sequence {xn​} converges to its infimum, we need…

Q: If n>1 prove the sum %3D is not an integer. 1无

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Q: Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.) i.…

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Q: (b) Decide the convergence or divergence of the sequence a = √8 and an+1 √8+ an.

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Q: Find the limit inferior and limit superior of the sequence {[5 sin n]}.

A: The given problem is to find the limit inferior and the limit superior for the given sequence of {[5…

Q: Examine the change of the function and draw its graph: 2x-1 y =

A: Given: The function in x is given,           y=2x-1x3ex-1x Objective is to find the change of…

Q: Find the limit of the sequences with general term as given: (a) n2 + 4n / n2 - 5 (b) cos(n)/n

A: Find the limit of the sequences with general term as given: (a) (n^2 + 4n) /( n^2 - 5)  (b) cos(n)/n…

Q: Is the sequence (N SIN N) properly divergent Is the limit +∞ or -∞0 ?

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Q: Suppose that the sequence x0, x₁, x2... is defined by xo = 3, x₁ = 6, and xk+2=-6xk+1-5xk for k20.…

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Q: 3. Prove that the sequence with nth un (a) is monotonic increasing, (b) is bounded above, (c) is…

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Q: Suppose (xn) is Cauchy and (yn) is bounded and monotone. Can we say anything about whether the…

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Q: uppose that the sequence x0, x1, x2... is defined by xo = 3, x₁ =0, x₂=5, and xk+3 = 13xk+1+12x for…

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