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

Q: 42. Prove that if lim "O = 5, then lim h(t) = 15.

A: It is given that To prove that

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: 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: п+(-1)" (2n + 1) Sn

A:

Q: Let n be a positive integer. For which n are the two infinite one- sided limits lim 1/x" equal?

A: Let n be a positive integer. for which n are the two infinite one sided limits limx→0±1xn equal. for…

Q: Prove that lim, Vn = 1.

A:

Q: Q: Prove ha中 Lim x" an %3D

A: we have to prove that the following

Q: Express the function n, lim n→+∞ 4k² in closed for and then find the limit. n³

A: We will first write this function in closed form then we will calculate the limit of the function.

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

A:

Q: 3. Solve for -). the lim |t In(1 +

A: The given expression of the limit is: limt→∞tln1+3t

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

A:

Q: Im( 8. Compute lim,-o m, if exists.

A: Let z = x + i y  Im ( z ) = y and  Re ( z ) = x

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>0  but not for α=0.

Q: Prove that lim (2a2 + 3r + 6) = 5 using the e, 8 definition of a limit. %3D a -1

A:

Q: Find the lim inf (xn) and lim sup (xn) of Xn=3-(-1)"

A:

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

A:

Q: Assume lim,→a f (x) = L. If f(x) > k, prove that L > k. Prove by con- tradiction by assuming L < k…

A:

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

A:

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

A: We will find the limit.

Q: Evaluate the following limit. lim 5e ti-i+5tan tk 5t t+4+5tan 5t lim 5e li- -i+5tan'tk = t+4 (Type…

A: Solution:

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

A:

Q: Show that lim Vn = 1. n-00

A:

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

A: Given the equation which to be prove

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: 5. Prove that lim Show your t→-2 t+2 complete solution.

A:

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: Let a and b be positive real numbers. Evaluate lim (ax – Vax – bx) in terms of a and b.

A: To evaluate limx→∞ax-a2x2-bx where a and b are positive real number

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

A:

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…

A:

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

A:

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

A:

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: e) Finally, prove that lim az-2 does not exist.

A: Use left hand limit and right hand limit to proof it

Q: Calculate the following limits using the factorization formula x" - a" = 1x - a21x"-1 + ax"-2 +…

A: Given: limx→ax5-a5x-a

Q: Suppose that the lim x2 flx)- Which of the follomng State ment cannot be true ?

A: We have to find which of the following statement can't be true.

Q: Exercise 7. Evaluate lim vn(Vn+1- Vn). n00

A:

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

A:

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

A:

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

A:

Q: 3 (c) Apply the monotone convergence theorem to evaluate Lim fn(x)dµ.

A:

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…

A:

Q: S 56sin(t)dt Evaluate the limit lim

A: Evaluate the limit limx→0 ∫0x56sint6dtx7

Q: Show that the following: Ifr> 1, then lim Vr -1 = 0.

A: We have to solve given problem:

Q: please help thank you

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

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: 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