The following picture shows several regular n-gons (n = 3,4, 5, 6, 8 and 9) inscribed in a circle of radius r. Let A(n) be the area of the regular n-gon inscribed in the circle of radius r. Find lim A(n).

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

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Q: Find the postive integec N such that implies 4 a) lim P = 10 000

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Q: 4. Determine the value of the following limit: lim 818 n k=1 k n² + kn

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Q: lim Va+l+v

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Q: Q: Prove that Lim %3D n-a

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Q: Use the fact that lim,ex = c and the result of Exercise 2 to show that lim,c X" = c" for any integer…

A: If the function is a simple function, the substitution of the point of limit into the function helps…

Q: 7x+8 3. lim (– In x0 X 4x +8

A: Given limit: limx→ 01xln7x+84x+8

Q: Suppose fé Ra, b]. Prove that b- a lim b- f(x) dr. k=1

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Q: - Find the value of the limit lim In(a/b) a-b In(a-b) b-a In(b-a)

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Q: In(r² + 5) (a) lim In(r+2)

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Q: Show that lim,→»(1+ e* for any x > 0.

A: To prove:

Q: Determine whether the following statement is true or false. If this statement is true, explain why.…

A: If limn→∞an=πthen an must be conversent. Reason- an is the fuction of n and when n is tending to…

Q: Find the limit.

A: The given limit is, L=limx→2+e32-x=limx→2+e-3x-2

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: Prove using the definition of limit. (a) lim n→+∞ (n − 1/n + 1)=1

A: For the answer, please see next step

Q: lim w ln 2 In 1 3w

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Q: Show that lim n->∞ (1 + x/n)^ n = e^x for any x

A: Express (1+ x/n)^n using e in the base

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

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

A: "Since you have posted multiple questions we will solve the first question for you. If you want any…

Q: Evaluate the limit. lim 2h+3 h245h+2

A: Topic - limits. The given limit is limh→−1 2h2+3h2+5h+2.

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

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Q: Calculate the following limits using the factorization formula x" - a" = 1x - a21x"-1 + ax"-2 +…

A: To find: limx→2x5-32x-2 Using the formula: xn-an=x-axn-1+axn-2+a2xn-3+.........+an-2x+an-1

Q: Find the limit. lim ] [*-In(9a+ 11) %3D

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Q: Use the definition of limits (ε-N) to show limn→∞ ((n/(2n−1)) = (1/2).

A: Find the subtraction value of sequence and limit

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: Evaluate the following limits.

A: Consider the provided expression, limn→∞n2lnnsin1n Evaluate the following limits. We can write as,…

Q: Determine the infinite limit. lim In(x2 – 25) 00

A: The given right side limit is: limx→5+lnx2-25 Consider, "h" is a very small positive real number.…

Q: Using the e - N definition of a limit, prove that 8n lim n+00 4 = 2 4n – 1 -

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Q: In(9x) (d) lim x2

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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: Prove the statement using the ε, ?  definition of a limit.

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Q: Compute the limit.  lim?→1  (?^2+4?−5  /  ?−1) Type in your answer as a whole number

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Q: The value of k such that x2 lim kx + 7 x→1 x – 1 exists is

A: Given: The limit expression limx→1x2-kx+7x-1, To determine: The value of k such that the given limit…

Q: (b) lim csc(r)

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Q: 6. Use the e, 8 definition to show that lim,2 x + 1 x+ 3 emlin

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

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Q: Evaluate The limil lim at4 X-4 (a) 1 ® Indefinite © er O d a >>

A: We have to find the required limit for the given function.

Q: Prove the following using the definition of a limit. n - 1 (a) lim 1 n+on+ 1 (b) lim (2x² − 3) = −3…

A: Given a) limn→∞n-1n+1=1b)limx→0(2x2-3)=-3c) limx→2-1x2-4=+∞

Q: Find the limit. lim e8/(5 - x)

A: Given,  limx→5+e85-x  We have to find the limit.

Q: Find the limit. (If the limit is infinite, enter 'co' or '-o', as appropriate. If the limit does not…

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Q: B. If k is any real number, prove or disprove that sinkx 1. lim x-0 kx = 1.

A: We will prove this by L'Hopital's rule

Q: Use formulas (3)–(5) to evaluate the limit.

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Q: (b) From part (a), we know that lim an exists. Compute it. n00

A: Given that a1=3 and an+1=12+an for each n≥1 Also, the sequence an is monotonic increasing and…

Q: With regard to the limit lim x² = 25, Find a 8 such that |x² – 25| < 10¬3 if 0 < |x – 5| < 8.

A: We are given limx--&gt;5  X^2 = 25 We have to find delta , and we can find it by applying definition…

Q: Evaluate the limit given below. lim 9ti+ 1²-16 1²-4t j+ k 2 (→ 4

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Q: 4. Use the definition of a limit to prove that lim z = a* for any real number a.

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Q: Find the limit. lim [In(9 + x) – In(1 + x)]

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Q: Let an = n n + 1 . Find a number M such that: (a) |an − 1| ≤ 0.001 for n ≥ M. (b) |an − 1| ≤ 0.00001…

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