2k • 2 (1 + ²4 ) ²/²/₂ n 30. For what value of b does the integral x² dx equal lim 2 (1+ n→∞ k=1 (A) b = 2 only (B) b = 3 only (C) b could be any real number. (D) There is no such value of b.

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A: Here I am attaching image so that you understand each and every step.

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A: # the expressions are printed twice , taking them once given a=23 and b=45 The value of a+b is as…

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A:

Q: Q4. Evaluate k=n 2k + n Lim k2 + kn + 2n² k=1 n-00 Show the details of your answer.

A: The objective is to evaluate the above expression.

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A: To evaluate: limx→5 5x+23 Let y = limx→5 5x+23 y = limx→5 5x+213

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A: To evaluate the given limit, first, we multiply the numerator and denominator of the given function…

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A:

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A: To evaluate limy→0(πy(e2πy−1)+πy−12y2) Rewrite the given expression:…

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Q: √√x²+2x dx= Select one: a. None of them b. (x + 1)√x² + 2x - 1 In ( x + 1 +√x²+2x() + C C. 1 +In 1 1…

A: The integral we are trying to solve is ∫√(x²+2x) dx. This is a non-standard integral and requires…

Q: 4. lim -0 A. -2/2 B. 1 C. 2 h D. Does not exist sin

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Q: Q2. Find the x² + y² lim (x, y)→(0, 0) √√x² + y² + 1 − 1

A: We have to solve above question and find  limit

Q: 2. Which of the following equations is (are) true? n 3i 1. Izdz I. rdr = lim (-²+ ²) (²³) 848 i=1 O…

A:

Q: (sin x)(15x4 – 5x + 8) Let f(x) = 4x Find the value of limr→0 ƒ(x), or state that it does not exist.

A: Given f(x)=sinx(15x4-5x+8)4x

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A:

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A:

Q: lim,+-1 f(x) = $1 # 1 affe # HE 3 52 #1 0 EM 0

A: The objective is to evaluate the limit.

Q: an =  (8n − 2)! (8n + 1)!   a1 =   a2 =   a3 =   a4 =   a5 =     lim n→∞ an =

A: Consider the given nth term an=8n-2!8n-1! Since, 8n-1!=8n-1 8n-2! So, an=8n-2!8n-1!=8n-2!8n-1…

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A: The given limit,limx→-3-x+1x

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A:

Q: 446 34. lim

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A: f(x)=24x−25Find f−1(x)

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A: To find the following limit.

Q: (42) For f(x) = -2r" + 5x° – 12x²5 + 10, the degree of f"(x) is

A: