5a) When p is a real number greater than 1, it can be shown that the improper 1 1 integral |dx converges to the value 0-1· Use this fact to determine the values of p for which this integral would converge to I) II) 20 b) If P is in the interval (0, 1), the improper integral ! dx will also converge. Use appropriate limit techniques and notation to show an example of this by 1 1 finding the value of 2/5

Q: 4) In each part, determine whether the integral is convergent or divergent. 5 3 D 00 √x dx b) 0 - dx…

A: Solution to the integrals.

Q: 2 4x 1 3 x2-4 dx

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Q: Consider the error formulas. IEl s 6 - a), -[max If"(x)|], asxsb Trapezoidal Rule 12n2 (b – a)5…

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Q: Please answer the bonus part as well

A: 1. **Finding Poles**: We first find the poles of the integrand, which are the values of \(x\) that…

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Q: Calculate  lim as n approaches infinity of the integral from 0 to 1 of (ncosx)/(n+ex) dx. Justify…

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Q: Limit Comparison Test x+4 dx 1 √x²+2 S₁

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Q: 27. tan'x sec x dx 30. tan r dt

A: the basic formulae must to solve these problems: 1) ∫xn dx =xn+1n+1+c2)d tan(x)dx= sec2(x) 3) d…

Q: Use integration by parts to prove the reductionformula.

A: Consider the following integration by parts formula: ∫uvdx=u∫vdx-∫dudx∫vdxdx ILATE Rule: We have two…

Q: Evaluate the definite integral: 6/x with the upper limit being 5 and lower limit 1

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Q: 5. 0 sin² x x² + 1 xp

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Q: thi Prove that the improper integral } ] docdy (1 + x² + y²) ³¹²/₂ Converges

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Q: Evaluate the integral f 2x (x² +1)** dx using the substitution 14 u = x² + 1. | 20 (a² + 1)“ dx +C

A: The given integral is: I=∫2x(x2+1)14dx Substitute u=x2+1 After differentiating,…

Q: Use the Comparison Theorem to determine whetherthe integral is convergent or divergent integral 0…

A: Introduction: The comparison test is a very important tool to test the convergence of an improper…

Q: Use the limit definition to evaluate the integral. Do not use the Fundamental Theorem of Calculus!…

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Q: How do I do this one?

A: Given integral is The integral is improper and can be evaluated as follows

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.