Letan =anlimn→∞ bn55n² + 14n3n5n²21'Calculate the limit.(Give an exact answer. Use symbolic notation and fractions where needed. Enter DNE if the limit does not exist.)bn||53n²ÌM8 IM8Determine the convergence or divergence ofn=1an.Σ an diverges by the Limit Comparison Test because lim is finite andann→∞ bnn=1anΣ an converges by the Limit Comparison Test because limn→∞ bnIt is not possible to use the Limit Comparison Test to determine the convergence or divergence ofn=1میگمan∞an converges by the Limit Comparison Test because limn→∞ bnn=1bn diverges.is finite and b, converges.is finite andn=1∞n=1bn diverges.an.

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Answered: Let an = an lim = n→∞ bn O Calculate…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Use the ratio test to determine whether ∑n=14∞4n(5n)2∑n=14∞4n(5n)2 converges or diverges.(a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n≥14n≥14, limn→∞∣∣∣an+1an∣∣∣=limn→∞limn→∞|an+1an|=limn→∞ (b) Evaluate the limit in the previous part. Enter ∞∞ as infinity and −∞−∞ as -infinity. If the limit does not exist, enter DNE.limn→∞∣∣∣an+1an∣∣∣limn→∞|an+1an| = (c) By the ratio test, does the series converge, diverge, or is the test inconclusive?
1. Consider the sequence Xn = √n + 1 − √n, n ≥ 1. Prove that (xn)n isconvergent. Find its limit.
1. Use the definition of the limit ( epsolon - delta ) to show thatlim of 1/z as z approaches -i2. Give the condition which ensure that |ez| < 1 where z in C.
Using the ε − N definition of a limit, prove that lim n→∞ (6n^3 −2n+1)/(2n^3 + 1) =3.
Let n be a positive integer. For which n are the two infinite one-sided limits limx→0±1/xn^n equal?
C. Suppose that (sn) and (tn) are sequences so that sn = tn except for finitely many values of n. Using the definition of limit, explain why if limn → ∞ sn = s, then also limn → ∞ tn = s. Explain this by just using definition of limit!Thanks
Let bn = an+1. Use the limit definition to prove that if {an} converges, then {bn} also converges and lim n→∞ an = limn→∞ bn
Hoping to get some help on #4 in showing the limit exists and finding it.
show that the limit of a^n/n! is 0 as n approaches infinity
Let fn: R --> R be defined by : fn(x)= x/(1+nx2), For all n >= 1. a) Show that {fn} converges uniformly on R to a function f. b) Show that f'(x) = limn -->infinity f'n(x), For all x does not = 0, but this equality is false for x = 0. c)What assumption in the theorem on the interchange of the limit and thederivative is missing? I am stuck with that last part (C).
Prove that limit of x^4cos2/x=0 , as x approaches zero.
Calculate the limit algebraically. (If an answer does not exist, enter DNE.) lim h→0 8h2 + h 3h2 + 3h - ________________ If the limit does not exist, say why. (If the limit does exist, so state.) -The limit does not exist because one side diverges to ∞ and the other side diverges to −∞. -The limit does not exist because only one of the left or right limits exists as a finite value. -The limit does not exist because the left and right limits exist but are not the same finite value. -The limit does not exist because it diverges to ∞ or −∞. -The limit does exist and is a finite number.

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