Given the relation an+1 a, + 12 with a, = 1, then lim a,- (a)3 (b)0 (c) 4 (d) 12 (e) None

Q: Evaluate the limit. 2² 4x+3 lim,>∞ 3x³ - 2x+3 01 O 1/3 0:3

A: Given: limx→∞ x2-4x+33x3-2x+3  To find: Value of the limit.

Q: Prove the limit statements

A: The given function is To prove

Q: L3x* -3x +b for all X, If bx < alx) evaluate lim 96x)

A: Concept:

Q: Determine the value for c so that lim f(x) exists. X-4 x2 - 9, for x4 The value of c is

A:

Q: If (x, y)lim(2, 3) f(x, y) = 4, can you conclude anything about f(2, 3)? Explain.

A: Assume the function z = f(x,y).First observe the value of the limit for x followed by y.

Q: Q2. Evaluate the following 4-x2 1. lim x-2 3-Vx2+5 t2+3t+2 2. lim t--1 t2-t-2

A: Given: 1. limx→24-x23-x2+52.limt→-1t2+3t+2t2-t-2

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: Evaluate the limit x2+19x- 48 lim x--3 x2-11x+42 O a. а. 0 b. None of these. С. 13 11 d. 00 е. 13 17

A: Limits

Q: Find lim x→3- x2 – 9 for o, -inf for -o, and DNE

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Q: Find the values of the constants a and b such that

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Q: e L'Hospital's Rule to find 2 +3x-4 lim a 4- 5x - 3x

A: Note: scince you posted multiple question. As per our guidelines we are supposed to solve one…

Q: . Let P(r) = 5x³ – 3rª + 3x³ − 9r + 5. Give a step-by-step € – 8 proof that - - lim P(x) = P(1). I→1

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Q: Show that |x2-4|&lt;e ,  when 0&lt;|x-2|&lt;e(5+e)-1 and prove limx-&gt;2 x2=4 by using these…

A: Note: The statement is verified by the ϵ-δ statement of limit.

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: Prove the limit statements Sx², X = -2 **-2 lim f(x) = 4 if f(x) I-2

A: Given, fx=x2x≠-21x=2 To prove: limx→-2f(x)=4

Q: 2. Evaluate the following limits. -7r-8 (a) lim 4x +5 (b) lim 100 3r2-3.r +4 (c) lim

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Q: Use the graph to compute the quantities asked for. ... -3 -2 A. lim Ax) = %3D B. lim (x) = %3D

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

A:

Q: if (7- 2w) < f (w) < (7 – w²), for – 1<w < 1. Find lim f (w). w-0 2 O 7 O 4 O does not exist O O…

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: Find the lim f(x) if, for all x > 13, 7x – 3 < fx) < 7x² + 4x

A: Given : 7x-3x &lt; fx &lt; 7x2+4xx2

Q: Use the definition to show that x2 + x -6 lim = 5. x - 2 4.

A: I have just used the definition of limit

Q: lim 2x* - 8x + 16 x--2

A: Given limx→-22x4-8x+16 =2(-2)4-8(-2)+16=2(16)+16+16=32+32=64

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

A:

Q: 372 + 6 Evaluate lim, -2r Select one: A. - O B. - C. A O D. С. уз

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Q: Evaluate the following limits. х* + 3х + 2 lim, 'x-1 v2 x² + 4x +3 a. x² – 2x lim, „2' Vx² +5- 3 b.

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Q: When demonstrating that lim x → - 0.8 5x + 4 %3| with M = 100000, which of the following 6-values…

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Q: What is the solution of the lim x--4 O 8

A: We have to evaluate the following limit: limx→-4x2-16x+4

Q: if x1 then lim,-1 f(x) is 3 if x 1 (b) 3 3. Let f(x) = (a) 1 (c) not exist (d) other

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Q: Let a be a real number. If lim, »0 47 = 8, VIta-Vā then which of the followings is the value of a?

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Q: The limit lim (x,y)→(4,-5) exists and equals to Select one: O True O False 25x²-16y² -5x-4y -40

A: Given the limit is  limx, y→4,-5 25x2-16y2-5x-4y.

Q: Q2. Evaluate the following 4-x2 1. lim x→2 3-Vx²+5 t²+3t+2 2. lim t--1 t2-t-2

A:

Q: If 6x s g(x) s 3x* - 3x2 + 6 for all x, evaluate lim g(x)- X-1

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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: For which value of n, does the lim -ny*+16n = 2 у-2 32-у5

A: Given

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: 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 lim n2 +00

A:

Q: What is lim (x? – 4x + 5)? O 1 O 2 O does not exist

A: To find÷limx→2 x2-4x+5    limx→2 x2-4x+5=22-42+5                           =4-8+5…

Q: if (7- 2w) <f(w) < (7 – w²), for -1 3wS1. Find lim f(w). 7 O 5 O does not exist O 2 O 6 O 4.

A:

Q: 3 - 5x - 2.r, if a >1 4 lim f(x) if f(r) = -3 4.r, if r <1 r³ – 1 †;

A:

Q: Evaluate the limit x2+ 19x-48 lim x²+9x+112 X- - 16 X a. 13 23 O b. 19 23 O C. 00 O d. None of…

A: The detailed solution is given below Thank you

Q: m An = {-: m e N}, ne N, where N are non-negative integers. What is lim inf An and lim sup A,? n-00

A: The given set is An=mn: m∈ℕ, n∈ℕ

Q: ) Evaluate the function  f(x) =x2   -(2x/1000 )for x=1,0.8,0.6,0.4,0.2,0.1 and 0.05 and guess the…

A: Given function, f(x)=x2-2x1000

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: Given that 2f(x) + 8 lim = 7, T- 6 then lim f(x) = Select one: a. O b.-4 Oc. 0 Od. 2

A: We have to find the following limit

Q: Prove the statement using the €, & definition of lim(x² + 2x - 7) = 1. →2

A:

Q: Find all values c such that lim x-2 2c²x 5c +1 x²-3x + 2 - exists. (a real number)

A: We say a limit exists if right hand limit and left hand limits are same. We have…