216 – x3 - lim x → 6 x – 6 - 108 O - 108 - 24 O 72

Q: In(2x) (a) Evaluate lim x+ In(3x-1)

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

Q: Prove that -x-1 lim (x +x +1 Is equal (1) Hint 1) Multiply and divide by facilities. 2) Multiply the…

A: The given expression of limit is:…

Q: 26. If [x] is the greatest integer in x, then what is lim [x+1]? 7111

A: As per our guidelines we are supposed to answer only first question kindly repost other queation as…

Q: Which of the following statements are correct? Choose all that apply. 1 does not exist b. lim 1 a.…

A: The given function is

Q: Evaluate |x2-41 lim X-2 X- 0/0 O Does not exist

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

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Q: 5. Evaluate the following finite or infinite limits. 5x²+3x+2 a) lim x- o 2x2-x b) -5x3+3x+2 lim x→-…

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Q: Suppose that lim, f(x) 0 and f(n) = an for all integers n> 1. %3D +00 Then, lim, 00 edn =0. Select…

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Q: Evaluate the limit. N 13i lim N-00 N2 i=1

A: First get the value of summation and use sum of first N numbers = N(N-1)/2

Q: - a) Evaluate lim x- - 2 3 + x x + 2 2.

A: First solve then apply limit

Q: When demonstrating that lim x → - 2 5x + 4 = – 6 with 0.1, which of the following 8-values suffices?…

A: Recall:   ε-δ definition:       let f be a function defined in a deleted neighbourhood of a. Then  a…

Q: Use the e-N language to show that, if lim a2n lim a2n+1 A, then lim an = A. n00 n00 n00

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Q: Let (.) be a sequence of real numbers and let B be the subset of R defined by B :- {A:nEN}. Let i eR…

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Q: Evaluate the following limit: lim 2²-25 x→2 2-5 O Does not exist. 0-7 07

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Q: Let α = 2 + √2 and β = 2 −√2. Then n ∈ N implies (a) α^n + β^n ∈N and α^n + β^n = [α^n] + 1, (b)…

A: Given:                    α=2+2 and β=2-2 To prove: ∀ n∈ℕ αn+βn∈ℕ and αn+βn=αn+1 limn→∞αn+αn=1

Q: Evaluate the following limits. In(1+ x²) 5. lim r-0

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Q: 16. Evaluate using L'Hospital's Rule. x3-216 a. lim X-6 (In x) b. lim 4x2

A: Given, Part a: limx→6x3-216x-6 If we put x=6 we get an indeterminate form, Therefore by using the…

Q: If lim azn = 72400 lim a2n+1 = L, then lim an = L 121400 1140

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Q: 12. Evaluate the following limit: 4x lim X--∞ A 2 -00 √/₁ 1x - 1

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Q: 23: Eva In x² x-1x²-9 Evaluate these limits: 1) lim.

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Q: In x Evaluate lim x→0 x2

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

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

Q: Evaluate m In x where m, p EN- lim X+1 p(x- 1)

A: Use the L'hopital's rule and simplify the limit.

Q: 1. Use an e-proof to justify each of the following. (-1)"=0. (a) limn→∞ n (b) limn→∞ = 0. n (c) lim2…

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Q: Evaluate the limit In(x) lim x²-21x+20 X-1 X O a. 21 1 O b. -19 Ос. 21 O d. None of these. е. 1 19

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Q: Evaluate each of the following limits. 1. lim [[ ]]+[[4-x]] X-3- 2r3+5 lim 2. x2+1 X-- 00

A: Here we have to evaluate the given limits  (1) limx-->3- [[x]]+[[4-x]] . (2)…

Q: #7.) Evaluate the following limits C a lim 4x2-36 X->3 2x-6 E by lim X-72 Climx-5 X-75 √x-1-2 A…

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

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 lim 700 (n-1)-1 + (n − 2) x^²-2 +...+ OB. undefined O.D. 22-1 ne2+7

A: Here, to evaluate: limx→∞xn+xn-1+xn-2+...+x(n-1)xn-1+(n-2)xn-2+...+x

Q: 10. Prove that if lim(x,) = x and if x > 0, then there exists a natural number M such that x, > 0…

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Q: Suppose that an > 0 and b, > 0 for all n N (N is a nonnegative integer). If we know that both an and…

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

A: limit=?

Q: 1-Evaluate each of the following: 1. lim 2 2. lim

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Q: The value of (* +5)(* +1)( - 1) lim * - 1 is O 20 O 6 O 12 O 2 O 72 30

A: The limit of a function need not be the functional value at that point. Consider a rational function…

Q: 2. Evaluate the following limit. V x² -9 lim 2х-6 X-00

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Q: Evaluate the following limit: 2-1 lim xーー2 x +1 O3 Os O-3

A: Put limit as it is or solve and put x->2

Q: Use the e-N language to show that, if lim a2n = lim a2n+1 = A, then lim an = A. n 00 n00 n-00

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Q: 37. Prove that lim x2 = 25

A: The given function is

Q: 1+ x Evaluate lim x x2 In -

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Q: 1 Evaluate: lim - In x X - 1 X-1 O-1 O 1 O 1 1 2 1/2

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Q: A mistake includes but is not limited to a false statement; a statement that is not a logic…

A: Please check step 2 for the solution.

Q: 4) Prove that if lim(x,) = x and if x > 0, then there exists a natural number K such that x, > 0 for…

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Q: Suppose that an > 0 and b, > 0 for all n 2 N (N is a nonnegative integer). If we know that both an…

A: We will discard the options by taking examples for the series. both the series satisfy the…

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

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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: Evaluate lim is O -1/2 O 1

A: Given limx→2x2-4x2+4

Q: The numerical value of the lim 1118 n+3 nln (2) is equal to *******

A: