5. Let x X for n-1,2,3,.... Then lim "n+ n- X n" n A) e B) e2 C) e D) e E) 1

Q: In formally proving that lim (x² +x) = 12, let ɛ > 0 be arbitrary. Choose 8 = min Determine m. m =

A: Definition used -         Limit using ε and δ -                      If limx→af(x) =L        If…

Q: Q: Prove that Lim %3D n-a

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Q: Determine whether the statment is true or flase.

A:

Q: c) Prove that lim z' - z +1-i =1- z>l+i z – 2z +2 2

A:

Q: 8. Let BC2, C C2 and define if n is odd, В, C, An if n is even. What is lim inf An and lim sup A,?

A: For the solution follow the next step.

Q: Prove that lim r(x)= where m = 0, 1, 2, 3. .. II

A:

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: Enter a whole or decimal number, or DNE for does not exist or undefined. lx-이 4 + | lim x →0-

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Q: Let A, = [n,n+ 1] and B, = [0,3+ [ for all n eN. 1. HL lim 42(A,) 2. PL B =2 MEN 3. PL An lim pz(A,)…

A: Here non of the options are correct.

Q: Suppose fé Ra, b]. Prove that b- a lim b- f(x) dr. k=1

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Q: 2.14 Show anx" + ... a12 + ao lim n an bn .. provided that b, # 0.

A:

Q: Show: ( (|fl2 – €)² < lim sup E If (n) < (I|fl2 + e)² , Where ƒ E C(R | Z; , c) n=-N

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Q: Prove using the definition of limit. (a) lim n→+∞ (n − 1/n + 1)=1

A: For the answer, please see next step

Q: (2) Show that Jo for a > 0 but not for a = 0. lim 818 √ne-na² da a lim √ne-na2 748 da

A: We have to show that,   limn→∞∫α∞ne-nx2dx = ∫α∞limn→∞ne-nx2dx  for α&gt;0  but not for α=0.

Q: 1. Prove lim, n+2n³+7 2 0, using the definition.

A: I have used only definition of limit of sequence

Q: 2. Let (X, A, μ) be a measure space. If {E} CA and E₁ E₂ E3 ..., then prove **** that (UE)= lim…

A: A limit is a value that a function approaches as the input approaches some value. Limits are…

Q: Compute the following limits if they exist ৪+ i2 Lim 2→-2i Lim Re 2

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

A: Given the equation which to be prove

Q: In formally proving that lim (x – 3x² + 3x) = 9, let e > 0 be x →3 arbitrary. Choose 8 = min(, 1).…

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Q: Use the definition of limits (ε-N) to show limn→∞ ((n/(2n−1)) = (1/2).

A: Find the subtraction value of sequence and limit

Q: Prove the following. (b) lim( Vn² +1 – n ") = 0 - (c) lim Vn? n) = } 1 2 ||

A: Prove the following limits

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: The numerical value of the lim n+3 nln (2) "→ ∞ \ 11 + 1 is equal to

A: We need to evaluate the value of the following limit limn→∞n+3n+1nln2 Formula Used: limx→∞1+axx = ea

Q: Use an appropriate definition to prove the following limits. g³ – 16x4 = 1 x + 2 9x² + 4 (а) lim…

A: We prove the given limits: limx→5+x+2x2-25=∞ limx→∞x5-16x4x5+4x2=1 limx→-∞9x2+4x+2=-3

Q: 5 42sin(t®)dt Evaluate the limit lim

A: the given limit is: limx→0∫0x42sint6 dtx7 we have to evaluate the given limit. limx→0∫0x42sint6…

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: 4e' + 3e-i lim t→∞ 5e' + 2e

A: NOTE: Refresh your page if you can't see any equations. . divide the numerator and denominator by

Q: If(z)- 니 < e. By definition Show that: lim, »1+i = - а. b. 4 lim = 2i. %3D 2- 1-i z2

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Q: 4. Evaluate the following limit or show that it does not exist. 1 lim 2 u +u,

A: To evaluate the limit,  limu→01u-1u2+u

Q: Prove that lim [V4n² + n – 2n] = -

A: Use rationalize to solve

Q: Prove that lim vn+1= 1. n-00

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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: Prove the statement using the ε, ?  definition of a limit.

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Q: Compute the limit.  lim?→1  (?^2+4?−5  /  ?−1) Type in your answer as a whole number

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Q: lim, ,0 Ttan(1/r)=? O a. Limit does not exists O b.0 O c.00 O d. 2 O e. 1

A: Given, limx→∞xtan1x

Q: 2. Evaluate the following limit. 2хy? lim (x,y)-(2,1) 3x² + y2

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Q: The following picture shows several regular n-gons (n = 3,4, 5, 6, 8 and 9) inscribed in a circle of…

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Q: Let m and n be two positive integers greater than 1. ecos (α"). am m then the value of (1) is n If…

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Q: 00 *tan(1/r)=? O a. 2 O b. 00 O c. Limit does not exists

A: You know:

Q: Prove that lim r = 2 using the e-8-definition. Hint: VI - 2 = VT + 2

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Q: 2х — 5 lim 4x

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Q: (b) From part (a), we know that lim an exists. Compute it. n00

A: Given that a1=3 and an+1=12+an for each n≥1 Also, the sequence an is monotonic increasing and…

Q: please help thank you

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

Q: Evaluate the limit given below. lim 9ti+ 1²-16 1²-4t j+ k 2 (→ 4

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Q: Find the limit. 8i lim n+ oi =1 O 20 O 10 O 16 O 8

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Q: Evaluate the limit. 1- r + In (x) lim I+1 1+ cos (3 7 x)

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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