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Q1 Determine S if the following integral converges or diverges: 1 dx. (2x-1)³

Q1 Determine S if the following integral converges or diverges: 1 dx. (2x-1)³

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q1 Determine if the following integral converges or diverges : 1 dx. (2x-1)³ Q2. Determine if the integral jinx dx converges or diverges. 1 Q3. Express into partial fractions. Hence obtain the sum of the first (k+3)(k+4) 3 n terms Sn of the series What is the value of S? k(k+3)(k+4)* Q4. Check to see if the following integrals converges. 1 00 Σ k=1(k+1)(In(k+1))² (b) Σ k=1 k (c) Σ- k=11+9k² Q5. Given two vectors a = <3, 2, 1> and b=<1, -3, -2>. Find (i) (a + b). (axb) (ii)the angle between a+b and axb. Q6. The points A(3, 4, 2) and B(3, 7, 2) are on a plane. If the plane also passes through the y axis Find (i) the equation of the plane (ii) the acute angle between the plane and the xy plane (iii) distance from point A to the line x = t y = 3t z = 1-5t
Transcribed Image Text:Q1 Determine if the following integral converges or diverges : 1 dx. (2x-1)³ Q2. Determine if the integral jinx dx converges or diverges. 1 Q3. Express into partial fractions. Hence obtain the sum of the first (k+3)(k+4) 3 n terms Sn of the series What is the value of S? k(k+3)(k+4)* Q4. Check to see if the following integrals converges. 1 00 Σ k=1(k+1)(In(k+1))² (b) Σ k=1 k (c) Σ- k=11+9k² Q5. Given two vectors a = <3, 2, 1> and b=<1, -3, -2>. Find (i) (a + b). (axb) (ii)the angle between a+b and axb. Q6. The points A(3, 4, 2) and B(3, 7, 2) are on a plane. If the plane also passes through the y axis Find (i) the equation of the plane (ii) the acute angle between the plane and the xy plane (iii) distance from point A to the line x = t y = 3t z = 1-5t
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