Let A.=(-11.1- and B. 4. for all n E N. 1. PL lim PL(A) 2 BUB. =2 3. AL lim u(A.) -3.

Q: Find o for e = 0.1 for the following limit. %3D lim 3x - 4 = 17

A: ε=0.1 and limx→7 3x-4=17

Q: In(x – a) For a e R, which statements do hold for the one-sided limit lim ? 1¬a+ In(e² – eª)

A: Here we use L'hopital's rule

Q: Show that (2o + h)" – 2ö = nz- | n-1 lim h→0 h for any zo E C.

A: To show: limh→0z0+hn-z0nh=nz0n-1for any z0∈ℂ

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

A: It is given that To prove that

Q: 1. Complete the following tables of values to investigate, lim(r² - 2x + 4). S(x) S(x) 0.5 1.6 0.7…

A: 1) limx→1x2-2x+4 x f(x) 0.5 3.25 0.7 3.09 0.95 3.0025 0.995 3.000025 0.9995 3.00000025…

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

A:

Q: b* – 1 Show numerically that for b =3 and b = 5, lim appears to equal In 3 and In 5, respectively.

A: Here given

Q: Find the value of lim f(z), if ƒ(±) = T-7+ 8z +4 7 O 16 O 9 6. O 21 O 35 O 49

A:

Q: (– 6 + h)? – 36 - Evaluate the limit: lim h→0 h

A:

Q: Evaluate the following limits. If needed, enter INF for o and MINF for 0. (a) lim (Væ? – – a 7x + 1…

A: (a)

Q: show that : Lim h→0  h / √5h + 4 − 2 =4/5

A:

Q: 8. Evaluate the limit dx lim C) E) 3 B) 1 D) 4

A:

Q: Find the limits in Exercis

A: Let f(θ)=θ cos θ. The limit exists if both the left-hand limit and right-hand limit are equal.…

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

A:

Q: S* 56sin(t")dt Evaluate the limit lim .8

A:

Q: Show that the following: If r > 1, then lim Vr – 1 = 0.

A:

Q: If A = lim ("C " C " C_ " C ……." C )m(a+1) then A² is equal to

A:

Q: -1 Evaluate the limit: limx→o tan ( Inx) Select one: TT а. 2 b. –1 С. d. 00

A:

Q: Show that for any &> 0 and Sn = 1X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. n-00

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

Q: 1. Find the following limit: lim (e + x)/

A:

Q: e the following limit by using defini ethods receives zero credit. 4n lim n00 3n -

A:

Q: Find the limit: lim, -/G) = . if f(2) = 23-1 %3D O (A) (3%+2,る O (B) (3%+2,る O (C) (3,+2) > O (D)…

A: We have to find Limit of given rational function.

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

A: Prove the following limits

Q: 5+ タイ m!7 (E Lim FIWO Lim tanx

A:

Q: Show with e and 8 that lim (t2 – t – 1, t? – 2t – 2) = (5,6) t→-2

A:

Q: Find the values of the following limits : V4+h 1-limn-0 h

A:

Q: Show that for any e > 0 and S, 1X₁, lim P(|S₁-81 ≥ 2) = 0. y'a 3140

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

Q: Find the value of lim f(x), if x→5+ S7x + 5 Зх + 4 f(x) = x 5 O 12 O 7 O 19 O 35 O 34

A: This question is related to limit .

Q: Find a o that works for ɛ = 0.01 for the following limit. lim 5z - 8 = 12

A: Given that: ∈=0.01limx→25x2-8=12

Q: Evaluate the following a) lim t-16 <VE-4, 1E+161, CON (16-E)) 16-t

A:

Q: e n Show that for any &> 0 and S, ₁X₁, lim P(S₁-0 ≥ 8) = 0. =

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

Q: Complete the following tables of values to investigate, lim(x - 2x +4). S(x) S(x) 0.5 1.6 0.7 1.35…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the value of lim f(z), if f(x) = 8x +3 z 7 %3D O 50 O 61 O 11 O 18 O 29

A: Limit of the function

Q: The function values for h(x) near x = 3 are given in the table below. 2.90 2.95 2.99 3 3.01 3.05…

A: Given Ltx→3-hx=1.45         Ltx→3+hx=2.45         Ltx→3hx=2.45 From table

Q: Find the value of lim f(x), if x→5+ S 6x + 3 f(x) = x 5 2x + 7 O 45 O 17 O 27 O 9 O 14

A:

Q: Which of the following limits is equal to a4 dæ? E(3+ 1 A lim n00 k= 2 B lim 3+ n00 k= 2k 3+ 1 lim…

A:

Q: O Determine the following limits O limx-0 3 1+y3x+1 sin 2x limx-0 10x"+x*+31 limx-too

A: We are allowed only 3 subparts of a question

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: 1. Complete the following tables of values to investigate lim(x? - 2x + 4). S(x) f(x) 0.5 1.6 0.7…

A:

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

A: we have to find the value.

Q: Find the following limit: 11a +31a 6. lim エ>0 6. Answer:

A:

Q: Is it possible to find numbers a, b and c so that an lim n+0o bn3 + cn erists but not equal to 0?…

A: Consider the function:

Q: 1. Complete the following tables of values to investigate lim,-1(x2 – 2x + 4) f(x) X 0.5 0.7 0.95…

A:

Q: Which of the following is equal to the limit lim ? x-0 x tan x O A. 8 В. 2 O C. 4 D. 0

A: We have to find the limit .

Q: Find the following limit: lim f(x) O A. 0 О В. О Ос. 3 O D. 4

A: We have to check

Q: Find the limit. lim ey sin P -(5, 0, -5) O 1

A:

Q: z2+e4Z lim Z→00 2z-ez

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: 1. Complete the following tables of values to investigate lim(x* – 2x + 4). f(x) f(x) 1.6 0.5 1.35…

A:

Q: What is the the value of the limit lim,o Vn (Vn +1– yn)?

A: Limit of the sequence

Q: Compute the following limits and write your answer to the boxes. lim 3x cot 2x

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.