lim e 11. In your own words, give an argument or a reason which justifies that n-00 n! = 0 where n! = n(n – 1)(n – 2)(n – 3).

Q: 1 a) lim n+00 V 0. 8 ) lim b) noo n+3 0. 5n2 – 3 (c) lim n0o 9n2 +4

A:

Q: Now prove the required result. For n=1 (1+x} 21+x[As 1+x=1+x] Let us assume the result for n=k…

A: Given a proof of the statement 1+xn≥1+nx for all natural number n, To Explain: The given proof of…

Q: 3n + 4 A) B) none of these 4 10n 3n +4 lim 4 10n #0 has NO HOPE of convergence since n00

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Q: Using the Nth term test for divergence 5 1 n=1_2n +14 5 diverges since lim is equal to 1 2n+14 O 1/3…

A: We can answer the question as below.

Q: 2. M is at -2 and N is at 14. Find the point X so that X partitions M to N in a 3:1 ratio.

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Q: nt b n+30 n+3 lim e + e nn+3 nn+3n

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Q: E an diverges and lim an/bn = 0, then b, diverges. n=1 If n00 n=1 True False

A: Limit comparision test

Q: 2n2 + 3 Let Sn ak. If Sn for each n > 1, which of the following statements is n2 +1 k=1 correct? (a)…

A: Given       Sn=∑k=1nakan=2n2+3n2+1  for each n≥1

Q: limit as n approaches +infinity of (n/(e)^n)

A:

Q: 8 Let k(x) = |x|", n = 1,2, ... Is k differentiable for all x and every n? Find a formula for k' (x)…

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Q: 5n – 9n3n lim (4п)2n + 17 n-00

A: Note the results : that is    Product rule of limit : If at least is one of them is non -zero…

Q: 4n+1 b] lim %3D n+3

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Q: If lim an 0 then an diverges n- 00 n=1 O True False

A: There is a theorem which states that: statement: if a series ∑n=1∞an of real numbers converges then…

Q: 4n +5 Describe the long run behavior of f(n) = 3nº – 5n° As n → – 00, f(n) → As n → 00, f(n) → Add…

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Q: -n 1 1+ 5n n=1 L = lim Vlan| (Enter 'inf' for .) E (1 + )" is: En=4 -n is: 5n OA. convergent B.…

A: According to question,Given series,∑n =1∞1+15n-n

Q: (a) Find the least positive k E N such that 3* =10 1. (b) Using this k, prove: for all m e N, 3m =10…

A: (a) find the least positive k∈ℕ such that 3k≡10 1 b) using this k prove that : for all m∈ℕ 3m≡103m÷k…

Q: (Зп+5 Find infimum of A |n E N} n+9

A:

Q: or a series of dependent trials the probablity of success on any traip is (k+1)/(k+2)

A: Given: for a series of dependent trials the probability of success on any traip is (k+1)/(k+2) Here,…

Q: = x3 + x - rith starting d with the of x after the

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Q: 0-6 3 Evaluate /e*dr by Simpson's th rule, taking n = 6. 8.

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Q: For the BVP to find the steady-state temperature in a sphere, we use Legendre polynomials in the…

A: Use the properties of Legendre polynomial to write the functions in terms of it. Use the expanded…

Q: z2 -1 What is residue of f (z) = at z=3 ? -8 Res (f(z),3) = 3 8. Res (f(z), – 3) = None 8 Res…

A: Since f(z) has simple pole at z=3, we use the formula to calculate  residue at simple pole, see next…

Q: 2n²+3n 2 3) Prove (with an e - N proof): lim n-0o 3n2+8n+2 3

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Q: a) They are all convergent b) 1 is convergent but II and III are divergent © II and III are…

A:

Q: e comergence y divergence harmonie Sesies Discuss the the of n=1

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Q: Suppose (xn) does not converge to 0. Then there exists e>0 such that all except for finitely many…

A: Consider the sequence xn=1,0,1,0,1,0,....... Here the odd terms are 1 and the even terms are 0.…

Q: Find the limit of s(n) as n o. 1n(n + 1) | s(n) n2 8

A:

Q: For any n large enough, prove E" ) – = 0(1). k=0

A:

Q: o-(2) 16. f(x) 15. f(x) = In In X 17. g(x) = (In x)4 (Hint: Use the Extended Power Rule.)

A: Extended power rule:

Q: e(z – 1) The residue of f(z) = at z = -9 is -9e-9 (6+2)

A: Detailed explanation mentioned below.

Q: Q 4. (a). Show that limit *1, does not exist if (5-4x S(x)=. -)- {ax-2 for x <1] for xz1]

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Q: Σ (-1)n+1 n3 n=1 11. Find an upper bound for the error in the above approximation |S – Sg].

A:

Q: (z- 1) The residue of f(2) = at z = -9 is -9e9 (z + 9) Select one: O True False

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Q: 3n? is strictly increasing and find an upper bound. n2 + 2 Rigorously show that a, =

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Q: es Mailings Review View 10.1 11. 1 12.1 13. 1 14: 17 Show from first principles that 2n – 2n² + 5…

A: To solve the limits of the function, Take out common the highest power of variable from numerator…

Q: -1 6) Show that tan N. converges/di verges. N2 N-1

A: Solution of question as follows

Q: (a) Prove that 0 n(n-1)(n-2) for eachn e N. [Hint: You may wish to use the function f(n) = n(n –…

A:

Q: 3n? is increasing. Find an upper bound. n2 +2 Show that an

A: Consider the sequence and check whether Sequence is increasing or not.

Q: For the part highlighted in green, why doesn't negative infinitiy cancel with the negative near the…

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Q: Q1:Proof the following Limits : C. Ln=1n! e-n

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Q: flx) = x (x-2)+g Eメとス ;if x22 Show that there exists a S such +hat 1x-2166 implies fex)-8<A

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Q: The expansion 1 + x + x² ... approximates (1 - x)1 if O x is not equal to 1 本 O absolute value of x…

A: The expansion 1+x+x2+.........approximtes 1-x-1

Q: 41. Can √5 be approximated through fixed-point iteration? Define a f(x) and a g(x) to do this if it…

A:

Q: 12 Σ 1 – x2 where 0 <x < 1. n=0

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Q: 2km+3(m+k)+4 E(Xkym) = (k+1)(k+2)(m+1)(m+2) where k and m are both nonnegative constants. Determine…

A: Given Using the joint distribution describing X and Y, the following formula was derived   where k…

Q: 2+ x²- 2x Given g(x)= and with po= 0.5 generate p3. 3.

A: In the given question, concept of Newton's Iteration is applied. Newton's Iteration The…

Q: 2+x²- 2x Given g(x)= and with po= 0.5 generate p1. 3.

A:

Q: Corollary 11.3.3. Suppose Do anc" diverges for some real number c. Then Eo anx" diverges for all æ…

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Q: Applying the ratio test to the series ∞ 1 k you would compute ak+1 lim = lim k→∞ k→∞ ak k=1 11

A: Given query is to apply ratio test.