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

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

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Q: Suppose lim, An = 1. Prove that 1 lim E(-1)*a2k = 0. n-00 n k=1

A: Given that limn→∞an=1. To prove limn→∞1n∑k=1n-1ka2k=0.

Q: 2n3 +1 1 Prove, using definition of limit, that lim 4n3 – n 2 n-00 -

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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. Select the best answer below: lim (2x-13 X (-1)* O -2 O does not exist

A: We have to find the limit and select correct option

Q: Find the limit. 2 – 4x². - 9x + 11 lim - 8x + 6x +2 X00 11 OA. 2 ОВ. оо OC. O D. 1 F/N 8

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Q: 1) Find the Limit lim/→0 3x²h-7th+h h

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Q: The value of the limit 3 lim (1- z/2 is equal to O e-3/2 O e3/2 O e2/3 O 1 The limit does not exist

A: Given: The limit limz→∞1-3zz2.

Q: 2) Use the e-8 method to prove lim (3x - 1) = 2 Given e > 0, there exists a d such that if 0 < |z-a…

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Q: Find the limit of (2n!/n!n!)^1/n as n approaches infinity

A: Here we find the limit of (2n!/n!n!)^1/n as n approaches infinity

Q: Solve for the limit: lim \belowx → 3 x2-9 O a. 1. 54 c. 6. 1 54 O d. 1/9

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

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Q: The value of the constant k such that .2 k x +7 lim exits is X - 1 X → 1 7 - 7 -8 -6

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

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Q: r+ 2 Calculate the limit lim 1-2 x2 – 3x – 10°

A: By using L'hopital's rule, we find the limit of the function.

Q: 6. Evaluate the limits. sin(0-4) а. lim Ө-0 Ө-4 4w b. im woo 20w+1

A: It is required to calculate the limits of the following expressions:For part (a):

Q: 7 Find lim E n-00 k=1 n+7k

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Q: Use the e-N definition of limits to show that 2n -15 lim = 1. %3D n0o 2n - 13

A: The objective to show that limn→∞2n-152n-13=1.

Q: 4. Find the following algebraically. -2x – 4x +4 a. lim x³ – 27 x - 2 b. lim V9x² +1

A: SOLUTION-

Q: Ql(i) Prove that Lim t* ... /2n²+1 2n²+n]

A: The series is Lim12n2+1+12n2+2+......+12n2+n=12

Q: Find the limit: o-4t 6. lim t→0 4 – 13' 17 + t to

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

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Q: 2+x 4. lim 3x-7

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Evaluate the limit 9n4 + 13n³ – 5n – 10 lim 25n16 +5n2 – 9n n00

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Q: 7. Find the limit. (Let c and d represent arbitrary real numbers. If an answer does not exist, enter…

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Q: Prove that lim [V4n² + n – 2n] = -

A: Use rationalize to solve

Q: 1. Solve the following limits. (a) lim T→-∞ V1 + x² x In x (b) lim x UJ + x 00x 2+ sec (3x) (c) lim…

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

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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: 10.2.29 Because 0.5 1. e 3+(1/3"-1)

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Q: Find the lim inf (xn) and lim sup (xn) of Xn = √1 + n² 2n - 5

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Q: Let an 2n+4n-3 Using the definition of the limit, prove that lim,∞ an 3n2+2n+1* 2/3.

A: Given that, the rational function  an = 2n2+4n-33n2+2n+1 To prove that limit of function is limn→∞…

Q: Find the limit 4x2+17x lim x+0 ex-1 a. 1 17 b. None of these. c. с. О O d. 17 е. 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: 5. Use the concept of limits to solve for the following problem iz3 – 1 lim z-1 z + i

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Q: In (n + 1)2 Vn lim n- 00 Select one: а. b. C. -1

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Q: 1. Use a table of values to estimate the limit correctly to the nearest hundredth. x' - 3x? +2x –- 6…

A: Please see the answer below.

Q: 2. Let x E (0, 1), use e – d to prove V4 +x – 2 lim 1 4

A: 2. Given x∈0,1, limx→04+x-2x=14                       ... (1) Use ε-δ definition to prove above the…

Q: Is In(x² – 1) - 1) 6. Evalaute lim n cos(x)-1 r lulx2-1) lem lulx²-1)

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Q: 1 Q5. Use the precise definition (i.e., via the e 8 notation), prove lim х-2- (х-2)3 = -0.

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Q: 1. Compute the indicated limits. Make sure to be very explicit about which results you are using in…

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Q: 1 11 lim X- 1 x2 + 9x – 10 Give your answer in exact form. If the limit does not exist, enter DNE.

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Q: The value of the constant k such that x2-kx+7 lim exits is x-1 x+1 -7 7 -8 8 -6

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Q: Find the limit. lim (e 4/x+ 9x) x/2 x-0 0 1 00 e2

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Q: A company training program determines that, on average, a new employee can produce  N( t) pieces of…

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Q: The value of the constant k such that x²– kx+6 lim exits is X→1 х—1 б -6 -7 7 -8 8.

A: 1). From the given problem:   fx=2x+14   From the power law:   dxndx=nxn-1.   So,…

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: In (3t) lim t2

A: Given : f(t) = ln(3t)/t² To find : Limit of the function

Q: -10 2468 10 x -4+ ad • +8- -10- Find lim f(x) = %3D

A: The graph of the function f(x) is

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.