2. Show that (+1 e2 lim n-o and lim arg 1+ NIR

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

A:

Q: In (e – 1) In x 34. lim

A: The limit which is to be evaluated is given by limx→0+lnex-1lnx

Q: Compute the following lim (h+5)2 + 25 lim

A: given

Q: 1. Compute lim. ( ). 1 x→2+ 2 x² – 2x. where c is a real number. You may need to discuss according…

A: limx→2+1x−2−cx2−2x

Q: What is limf(x) as shown in the graph? AY 1.14+ 0.76 0.38 -4a -3% -1% 2n -0.38 0.76 -1.14+ O -1 O 1…

A: The graph of f(x) is as shown below :

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

A:

Q: 1. Find the limit of the following: х* — 11x5 + 37x* +6х3 — 297x? + 621х — 405 - lim,-3 А. x→3 x° —…

A:

Q: Show limn→∞(1 +1/2+1/3+···+1/n−lnn) exists

A:

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 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

A:

Q: can this be evalnated by using L'HOSpital's Ruie? lim Trxln(x) Itxen(x) (メ-)nx

A: The given limit can we evaluated by using algebra of limits.

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

A:

Q: EX.3: Use the M-N definition to show that lim (n - 10n2 – 6n + 3) = 0.

A: According to M-N definition, Let, an=n3-10n2-6n+3                                 ...1if…

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

A:

Q: Consider the following list of conjectures. Provide a shortproof for those that are true and a…

A:

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: Find the following limits: 10 +10n 10 lim n00 1+2n+3n2 +4n+10n10 lim n/ 71

A:

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

A:

Q: The numerical value of the lim 31-0 Question 1 n+3 nln (2) n+1 is equal to

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

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: In formally proving that lim (2² + x) (유, 1). = 42, let e > 0 be arbitrary. Choose 8 = min Determine…

A: Given limx→6x2+x=42 Consider x2+x−42=x2+7x−6x−42=xx+7−6x+7=x−6x+7≤x−6x+7 Hence, x2+x−42≤x−6x+7.....1…

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

A:

Q: Use the definition to show that 4n – 5 lim 2n + 3 - 2. n00 3.

A:

Q: 1-a limz→1 =? O -2 O 1 O Does not exist

A: find limit

Q: In(z – 7) Evaluate : lim i In(e" – e7)

A: Given: limx→7lnx-7lnex-e7

Q: In c lim m>0 is Select one:

A: To determine the value of the limit.

Q: 1. Use the definition to establish each of the followii (a) limx→2(2x– 7) = –3 (b) lim→1 T = (c)…

A:

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: 3. If we know that > ak = 10,000, then what can we way about lim ay? %3D k=1

A: Explanation of the answer is as follows

Q: In(x)-In(a) 14. lim %3D Xa X-a (A) = (B) In(x)NT 92 anevni art

A: Given, limx→ alnx-lnax-a

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

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>0 there is an integer N such that                   |an-L|<ε…

Q: Prove that lim n = p.

A:

Q: if it wass and %3D + 2 H nEN 2 then lim (Xn)

A: In the given question we have to find the limit of the sequence xn as n→∞and the recurrence relation…

Q: Calculate the lim sup and lin inf of the following: √1+n² 2n-5 1. Xn 2. Xn where yn is bounded 3.…

A:

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

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

Q: 1. Use L'Hospital's Rule to compute In(1+x) – lim | x2 2 Compute

A:

Q: In(x – 6) In(e# – eº) Evaluate : lim

A: limit=?

Q: Find the,* x2 - 1 lim I-1- x2 + 5x + 4 O -2/3 O 10 O undefined

A: We will solve the given limit.Below find the solution in the image.

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

A:

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

A:

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

A:

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