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7-9 Find the length of the curve correct to four decimal places. (Use a calculator to approximate the integral.) 7. r(t) = (1², 1³, 14), 0≤ t ≤ 2

7-9 Find the length of the curve correct to four decimal places. (Use a calculator to approximate the integral.) 7. r(t) = (1², 1³, 14), 0≤ t ≤ 2

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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2. r(t) = (21, 1², 1³), 0≤1≤1 3. r(t) = √√2ti + e'j+ek, 0≤ t < 1 4. r(t) = cos ti+ sin tj + In cos tk, 0≤ t ≤m/4 5. r(t) = i + t²j+t³k, 0≤ t ≤1 6. r(t) = t² i + 9tj + 413/2 k, 1≤ t ≤4 7-9 Find the length of the curve correct to four decimal places. (Use a calculator to approximate the integral.) 7. r(t) = (1², 1³, 14), 0≤ t ≤2 8. r(t) = (t, e, te ¹), 1≤ t ≤3 9. r(t) = (cos πt, 2t, sin 27t), from (1, 0, 0) to (1,4, 0) 10. Graph the curve with parametric equations x = sin t, y = sin 2t, z = sin 3t. Find the total length of this curve correct to four decimal places. q 11. Let C be the curve of intersection of the parabolic cylinder x² = 2y and the surface 3z = xy. Find the exact length of C from the origin to the point (6, 18, 36). 12. Find, correct to four decimal places, the length of the curve x + y + z = 2. of intersection of the cylinder 4x² + y² = 4 and the plane 13-14 (a) Find the arc length function for the curve measured from the point P in the direction of increasing t and then i reparametrize the curve with respect to arc length starting from P, and (b) find the point 4 units along the curve (in the direction of increasing t) from P. 13. r(t) = (5-1) i + (4t-3)j + 3t k, P(4, 1, 3) 14. r(t) = e' sin ti + e¹ 11 1 1 2 2 2 8 : :
Transcribed Image Text:2. r(t) = (21, 1², 1³), 0≤1≤1 3. r(t) = √√2ti + e'j+ek, 0≤ t < 1 4. r(t) = cos ti+ sin tj + In cos tk, 0≤ t ≤m/4 5. r(t) = i + t²j+t³k, 0≤ t ≤1 6. r(t) = t² i + 9tj + 413/2 k, 1≤ t ≤4 7-9 Find the length of the curve correct to four decimal places. (Use a calculator to approximate the integral.) 7. r(t) = (1², 1³, 14), 0≤ t ≤2 8. r(t) = (t, e, te ¹), 1≤ t ≤3 9. r(t) = (cos πt, 2t, sin 27t), from (1, 0, 0) to (1,4, 0) 10. Graph the curve with parametric equations x = sin t, y = sin 2t, z = sin 3t. Find the total length of this curve correct to four decimal places. q 11. Let C be the curve of intersection of the parabolic cylinder x² = 2y and the surface 3z = xy. Find the exact length of C from the origin to the point (6, 18, 36). 12. Find, correct to four decimal places, the length of the curve x + y + z = 2. of intersection of the cylinder 4x² + y² = 4 and the plane 13-14 (a) Find the arc length function for the curve measured from the point P in the direction of increasing t and then i reparametrize the curve with respect to arc length starting from P, and (b) find the point 4 units along the curve (in the direction of increasing t) from P. 13. r(t) = (5-1) i + (4t-3)j + 3t k, P(4, 1, 3) 14. r(t) = e' sin ti + e¹ 11 1 1 2 2 2 8 : :
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