7. Suppose lim nan = A +0 where an is not necessarily nonnegative. Prove >a,n diverges. n=1

Q: B. Prove the fillang tim Jn2 +n 4- (6) lim n-700 Lvntl trn

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Q: If lim [sin(zn)] In z 4 for n > 0, find the value of |3D n. In 4 In 2 4 1

A: Take ln both side and use l hospital rule

Q: Compute the following limits using l'Hospital's rule if appropriate. Use INF to denote o and MINF to…

A: NOTE: Refresh your page if you can't see any equations. . use L'hospital's rule

Q: Use L'Hopital's to determine the limit. lim Oo O1 ○ -1 enx ~|-1 as x approaches co

A: This question can be solved using the concept of L' Hopital's Rule and derivatives.

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Q: Pick 8 of 10: Prove or provide a counterexample. lim Sn =0 if and only if lim s,=0

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Q: Compute, from first principles, without using L'Hopital's rule eh – 1 lim = 1 h-0 h

A: (18) We have to evaluate the limh→0eh−1h. We know that the expansion of eh, which is given by…

Q: 7 Find lim cos - Enter I for o, -I for –∞, and DNE if the limit does not exist. Answer:

A: Given query is to find the limit of the expression.

Q: Compute, from first principles only, without using L'Hopital's rule eh - 1 lim = 1

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Q: Suppose that a, > 0 and converges. lim na, = 0. Prove that Ea, n 00

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Q: 1) @) Prove that lim an= o if lal <1 and a ER 6) show fon any X with Ix) <1, lim nxn=0- that

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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: 3. Show that the funtions f (x) = cos(/²+E) is continuous on R. Then compute the following limit 2…

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Q: Find the limit HI6) im [In(2 t+x) - In(1+x)] www

A: We will find the limit.

Q: 5. Suppose that limn00 Tn = 3. Prove directly (i.e. NOT by applying limit laws) that limn→o = 3.

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Q: Suppose that an<0 for all n, and define b,=tan-(a,-n). Then the sequence {b,}... O diverges to - O…

A: Solve the following

Q: Compute limit as x goes to infinity of (cos(x))/(x)

A: We find: limx→∞cosxx We solve this limit by using Squeeze theorem. Squeeze theorem states that if…

Q: Show that Hint: Use to obtain In[|x|] √√2/T. 1 - cos(sx) x² 8 1 - cos" x x² lim n-√√n 00 2 π dx |s|…

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Q: In(7)/ In(x) (17 + 8x?) Find lim Limit is equal to (Type an integer.)

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Q: 4x In z (a) Evaluate lim エ→1( (1- 2)-- -1) C.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: what is the limit as n goes to infinity of enn! divided by nn?

A: Since e^n &gt; n And rate of convergence (e^n × n!) &gt; rate of convergence (n^n)

Q: Compute the following limits using L'Hospital's rule if appropriate. Use INF to denote o and MINF to…

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Q: min 1) In formally proving that lim (x + x) 42, let e > 0 be arbitrary. Choose & %3D Determine m. m…

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Q: Suppose that a, > 0 and lim a, = ∞. Prove that Sa, diverges.

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Q: 5. Use L'Hopital's rule to evaluate e* +2 limy-o ex +

A: limx→∞ex+2xex+5x

Q: 8. )Prove that lim Vr = 2 using the e-8-definition. Hint: VI – 2 = x- 4 VI + 2 Puouo thot thoro…

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Q: a. Assuming that lim,(1/n') = 0 if c is any positive con- stant, show that In n lim n° п—00 if c is…

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Q: (7) ifa lim has a point that the equalio- prove PCz,y) is above L and only if 3x +2y >4

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Q: Prove ca) lim (an t anay t --- + that if Ean Converges, then + antr) = 0, (b) Give o7Convergence…

A: We have to use properties of convergent series first.

Q: Since this expression holds for all e, we must have fESSr. 25. Since fn <f on E for all n, we know…

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Q: lim el -1 dt 61-12-e

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Q: Зп+2 Determine the limit l= lim u, if un such that Jun – 1| N. " Justify your answer by identifying…

A: Given : un = 3n + 2/( 4n - 3)

Q: 4. Use the limit theorems (or homework from 4.1) to show that lim (Vn2 +n – n) converges. Hint: Do…

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Q: Express the following limit as an integral. lim 1-00- TL i=1 (2 (27)¹ + 3) 8-91 Ar over [1,6]

A: Note : As  per our guidelines we are supposed to answer only one question if there are multiple…

Q: Compute the following limits using l'H\^op to denote co and MINF to denote -o. 1 – cos(3x) lim x-0 1…

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Q: Cary) >Co,0) 4 + y2

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Q: prove that by using is linear oper aton the limit properties ?

A: A function is a linear operator if it satisfies the following properties: fx+y=fx+fyfcx=cfx We are…

Q: show that If an > 0, n = 1, 2,. .... In+1 In+1 lim inf 14x <lim inf n ≤ lim sup Van ≤ lim sup nx In…

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Q: Suppose an 20 and limnan = L.Then 1. If 0 ≤ L < 1, then Enz1an converges

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Q: please help thank you

A: We need to prove the given statements, which are,

Q: Express the limit lim > (7 sin (27) + 6)Az, over [2, 4] as an integral TL 00 1-1 Provide a, b and…

A: Formula :

Q: Express the following limit as a definite integral. 1 Σ 2-2 IPl-0 k=1 lim Ax, where P is a partition…

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Q: 18. Compute, from first principles only, without using L'Hopital's rule eh – 1 lim h-0 = 1

A: given is  limh→0  eh-1h=1we know    eh  = (1+h1!+h22!+h33!+.............)limh→0  eh-1h = limh→0…

Q: Find the limit of the following: lim In(3+ex)-In(9+x)

A: Use the properties of lograthim first than put the limit.

Q: Evaluate lim S", r³dx . O 4 Does not exist.

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Q: Compute the following limits using l'Hospital's rule if appropriate. Use INF to denote o and MINF to…

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Q: 6. Evaluate the following limits. arctan(z) – /2 (A) lim In (1-!)

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Q: 2. If (xn) and (Yn) are sequences of real numbers such that lim (xn) + 0 and lim (xn Yn) exists,…

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