If lim an 0o and En1 a, diverges, then E b, diverges O True O False

Q: 4. Let 1 4- t ift 2 Find the value of c so that lim B (t) exists. t-2

A:

Q: Let a, be recursively defined by ao = 3, an+1 = a - an for n 2 0. Find lim an.

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: If 0 < a <1, then lim(a)* = x00

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: 00 Let a, = 1- /1 -. Show that lim an = 0 and that > an diverges. Hint: Show that a, > 2n n=1

A:

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: If If(x) < B[ for all x in an interval containing 0, show that lim x?f(x) = 0.

A: if fx≤B⇒fx≤B for all x in an interval containing 0 show that limx→0x2fx=0

Q: 12 12 None of the alternatives are correct · (1¹)) = If L <=lim In then f(t) is 042

A:

Q: Find the lim x→2x-2 x2-4 O 3/4 O 1/4 None of these O undefined

A: Given query is to find indicated limit.

Q: If lim, va f(x) = lim, »a+ ƒ(x), then lim, »a f(x) does not exist. Select one: O True O False

A: Since we are given with multiple number of question answered according to the guideline,.

Q: If lim f(z) = 20 and lim g(z) = 26 then lim[3f(z)g(z) – 5] = O 1560 O 40 O 1555 O 1565 190

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Find lim an if an = n!+3" 1+n OA. 0 B. C. 00 D. OE. 1

A:

Q: If lim f(z) = o and limg(z) = 00 , then lim (f(x) – g(x)) 0. Select one: O a. False O b. True

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Q: that Find the implhes positive N such h > N ) lim E = 0.01 h -a 00

A:

Q: Let 7. B(t) = ift < 2 - Vt+c ift 2 2. Find the value of c so that lim B(t) exists. t+2

A: This question is based on limits.

Q: If lim f (x) = L, then ſa) = L. x-a

A:

Q: Show that if lim(a /n) = L, where L > 0, then lim(a,) = +0o.

A: Consider the given information: limn→∞an/n=L,  L&gt;0 To show that limn→∞an=+∞.

Q: Show that if lim,→m aŋ = 0, then O(a, + 1) = 0(1). %3D

A: This is a problem of real analysis, complexity.

Q: Iff(x)= a,x". x"+....+a,x+a, - with a 0,b>0 b x"+..+b,x+b, m m Then show that limf(x)=oif n>m x→0

A:

Q: define sequence a, by SELECT A A) B) lim a, =0 = 5-5t.5 C) -times %3D D) E) lim a F) lim a, = e

A: The given sequence is an, where an=555.....    (upto n times) We have to express this sequence as…

Q: n that so that they form a rigorous assertion that lim X-

A:

Q: 1. (f Use "e- N"-statement to prove that lim n 1 [Hint: Ve > 0,3N(e) = > 0, Vn > N, we have n- %3D

A: We have to show that given limit of function converge to 1-

Q: Evaluate r (n+) lim as n- 00 VnT (n+1)

A: Question: Evaluate: limn→∞Γn+32nΓn+1

Q: If lim, +00 an 0 or lim,,00 a, does not exist, then an diverges. Select one: O True O False

A:

Q: Demostrate that lim =o (1>a>o) 1 + €eo

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

A:

Q: tan(2x) x+02sin²(x) Evaluate: lim O a. ∞ O b. -∞ O c.0 O d.-1

A: We have to evaluate limx→0- tan2x2sin2x         Here two sided limit does not exist.…

Q: Suppose Σto an no an5. What is the value of lim a,? 72-0

A:

Q: If lim f(z) = 16 and lim g(z) = 25 then lim(3f(z)g(2)-71 = 1207 O 1200 O 1193 O 32 O 223

A:

Q: 11. If 0 < a < b, determine lim Qケ+! a" + b"

A: First we take comman bn+1  from numerator and bn  from denominator and then we  use lim ban=0.

Q: If lim (1,9) (a,b) f(x, y) = L and f is defined at (a, b), then f(a, b) = L. True False

A: Step:-1 Statement:- If limx,y→a,b f(x, y)=L and f is defined at (a, b), then f(a,b)=L Iff(x, y)  is…

Q: If lim g(x) = 13 and lim h(x) = 23 then %3D [39(x) + 6h(x)] lim x6 2 O 26 O 88.5 O 46 O 36 O 19

A: The limit of a function at a point exists if both left-handed and right-handed limit exist and are…

Q: Let x - for n - 1,2, 3, .... Then lim l equals O ve3 Oe-! Ove

A: we have to find the value.

Q: 12. Let L = lim a>0. If L is finite, the (A) a=1 (B) a=2 (C)L- (D) L-

A: We are asked to find a value and L values.

Q: Theorem 8. If lim a, = a and lim b, = b, then lim (a,b,) = ab. %3D

A: L

Q: 30. Suppose that f, f', and f" are positive on R. Prove that lim f(x) = 00.

A: Let f, f' and f'' are positive on R. We need to prove that limx→∞fx=∞ Consider, the interval [a,∞).…

Q: E. Show that if lim,-co an = 0, then O(a, 1) = O(1). %3D

A: given that  Limn→∞ an=0 now we find that Limn→∞-(an+1)

Q: ven that lim f(z) = 1 and lim g(z) = -4, evaluate the following. lim (-4f(z) – 2g(x)) z-1

A:

Q: For a ER and nEN, lim O (A) True. O (B) False. a" = 0 if | a|>1.

A: Thanks for the question :)And your upvote will be really appreciable ;)

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

A: We have to solve given problem:

Q: Let a>o be a Fixed real num ber. Evaluate: lim X-> a X - a ln Că).

A: limx→axx-a-1lnxa

Q: 4. Show the identity 1+ = (1+) (1+), then use it to prove n+1 (1+ 2) - = e?. lim n 00

A:

Q: Let 1 9 ift < 5 B(t) = 5 √t+c ift ≥ 5. Find the value of c so that lim_ B(t) exists. t-5 -

A: This question can be solved using the concept of limits.

Q: (g) Let fG) be diffaentioble and lim fC) = 00 If lim :o then lim fGJ=00or lim fCJ= -0 True O Fo lse

A:

Q: Evaluate I (n +) lim as n → ∞ VnT (n + 1)

A: Given: limn→∞Γn+32nΓn+1

Q: Evaluate lim is O -1/2 O 1

A: Given limx→2x2-4x2+4

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

A: