1-e¬* lim x→0+ 2x2 -00 00 None of these O 1

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

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Q: 2. Evaluate the following limits. 3x+5 e. lim x→+o 2x+1

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Q: Find the limit: 5 cos(n) (8n-1)(n+10)) lim + n- 00 in 9n2+n+3 ||

A: on solving this we get the

Q: -) lim 2ma 1 1 In x x² – 1 x→1 |

A: Given that: limx→112lnx-1x2-1

Q: 2) Use the e-8 method to prove lim (3x - 1) = 2 Given e > 0, there exists a d such that if 0 < |z-a…

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Q: Evaluate the following limit 6n+14 limn0 3n+11 n→∞ 3n+11

A: We  need to evaluate the limitlimn→∞6n+143n+11

Q: 2. Evaluate the following: Va2-x² So Sa* x² ydydx а. xsin x b. lim-2cos x+e

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Q: Evaluate I (n +) lim as n → 0 Vn[ (n + 1)

A: We have to evaluate limn+32n⋅n+1 as n→∞ that is limn→∞n+32n⋅n+1 We know that n=n−1! Hence,…

Q: Evaluate the limit: 3-7n +9n lim (5n-8)(1 In² + 4)]

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Q: In (1+7) lim t t→+0 t1/2

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Q: When demonstrating that lim 5x +2 = -3 with e = 0.2, which of the following 8-values suffices? r -1…

A: Topic:-Limits As per our guidelines, only one question will be answered at a time. please repost for…

Q: Exercise 1. Evaluate the following limits. e3x – e-3x а) lim x→-o e3x +e-3x b) lim [In(1+ x?) –…

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Q: 2) Calculate lim ( In(3x + 1) – In(2x + 1)). -

A: Since you have asked multiple questions, we will solve the first question i.e., Question-(2) for…

Q: 2 then E " Cn+1 converges. 3.11 limnr+m

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Q: 2+ 1 ** Evaluate lim - X+ oL dt A B none of these 1- e? 1 4

A: Given that,  Now taking the integral term,

Q: Present a “DELTA – EPSILON" proof, proving: prove th the de lim (3x – 7) = 5 X-4

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Q: Give the following infinite sum and limit: 8 2n-1 3n+2¹ n=4 a) rsin r (b) lim 20 x² + e²-1

A: The infinite geometric series states that ∑n=k∞rn=rk1-r, where r&lt;1. Simplify the expressions of…

Q: 15.) Show that lim((2n)/"): 1/m =1.

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Q: Prove that lim (1/ nP) =0, p> 0.

A: Given the equation which to be prove

Q: 19 let ɛ > 0 be arbitrary. Determine & as a function of e 2 In formally proving that lim -x + 8 1/4

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Q: 1. Use an e-proof to justify each of the following. (-1)"=0. (a) limn→∞ n (b) limn→∞ = 0. n (c) lim2…

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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: Prove lim(Vn+1- n)=c 8. 0 =

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Q: Prove or provide a counterexample to the following if r ∈ ( 0 , 1 ), then lim n→∞ r^n exists.

A: limn→∞an=L if for every number ε&gt;0 there is an integer N such that                   |an-L|&lt;ε…

Q: 10.2.29 Because 0.5 1. e 3+(1/3"-1)

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Q: 5. Evaluate the following limits. (a) lim (1+ e-2")3e²r+*. (b) lim (0.999999999)- In. |

A: 5(a) The given limit is: limx→∞1+e-2x3e2x+1 To evaluate the given limit.

Q: 1 Assume that lim xn +oo. Prove that lim n-00 n +o0. n-00 k=1

A: Given limn→∞xn=+∞

Q: Extend the result proved in Example 2.5.3 to the case |b| &lt; 1;that is, show lim(bn) = 0 if and…

A: We have to show lim(bn) = 0

Q: Suppose that an > 0 and b, > 0 for all n N (N is a nonnegative integer). If we know that both an and…

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Q: Question 11 Evaluate the limit lim (ln(3x² + 2) - In(x² + 1)) O ln 3 O In 3 01 00 O ∞

A: To evaluate the following limit.limx→∞ln3x2+2-lnx2+1

Q: 1. Show that for all f e L'(R) lim

A: To show: limδ→1∫f(x)-fxδdx=0 Concept used: ∫fxdx=Fx+c Chain rule: ∫fxadx=1aFx+c

Q: e -e lim is z0 In(1+ 2x)

A: Given limit:

Q: 8. lim In(+h)–1 A. 0 B. - C. 1 e D. e E. Does not exist

A: To solve the limit.

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: please help thank you

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

Q: 1² +1 Use the e-N definition to prove that lim = 1. x² + x + 1

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Q: 2. (a) Evaluate 7n+1 +2" i. lim N; n-00 7" – 2n | ii. lim Vn2 + 3n – Vn2 – 3n |, n € N, n > 3. n-00

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Q: In(x), 5 s x s 16 f(x) A = lim n- o 2 i = 1

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Q: 2 39. Prove that lim x"cos = O. X-0 X

A: The given limit to be proved is

Q: 1 Q5. Use the precise definition (i.e., via the e 8 notation), prove lim х-2- (х-2)3 = -0.

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Q: 1.9 Exercises 21 4. Suppose An = (-: m e N), ne N, where N are non-negative integers. What is lim…

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Q: Prove: If E an converges, then lim an = 0. n-00 Prove or disprove the converse of it.

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Q: Now, in in lim n → o n i = 1 30i -9 + lim n → o n 30 -9 + = 1 i = 1 But s -9= and i = 1 i = 1

A: limn→∞6n∑i=1n-9+30in=limn→∞6n∑i=1n-9+30n∑i=1ni=limn→∞6n-9n+30n×n(n+1)2  ; ∑i=1n-9=-9n  ,…

Q: a) Show that for any & > 0 and S₂ = ₁X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. n n→∞

A: We will use Chebychev's inequality to find the limit of the given probability.

Q: 3 In(z) Carefully define lim 21 2-I = 3, including phrases with e and d. %3D

A: Note that lnx&lt;=x-1  I have used that inequality to prove the statement

Q: In (3t) lim t2

A: Given : f(t) = ln(3t)/t² To find : Limit of the function

Q: 1. By introducing suitable limiting processes in 1 8(x) = 27 eikr dk, show that (a) 8(x) = 1 1 lim…

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Q: 7. Suppose lim nan = A +0 where an is not necessarily nonnegative. Prove >a,n diverges. n=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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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.