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30-31 At what point does the curve have maximum curvature? What happens to the curvature as x→∞? guitaluseo 30. y = In x TUJ02 sill to akihin si-62. 31. y estonio

30-31 At what point does the curve have maximum curvature? What happens to the curvature as x→∞? guitaluseo 30. y = In x TUJ02 sill to akihin si-62. 31. y estonio

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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A to sasiq yd boninnatab onslq sT T 17-20 srl mon estos smen od t≤ 5 q art gainianos niainos tadi sasia sib to sasly griminos0 t≤ 1 bidw browe!) 2017 0 < t < π/4 bolts *3 <4 ap to four decimal places. gral.) 4900 (1, 0, 0) to (1, 4, 0) ations x = sin t, length of this curve the parabolic cylinder nd the exact length of C 5). the length of the curve 2 y² = 4 and the plane or the curve measured sing t and then c length starting from curve (in the direction P(4, 1, 3) K, k, P(0, 1,√√2) = ) and move 5 units 2t 1² + 1 3 cost in the posi- j istros is onsl point (1, 0, 0). 2006 JOH (b) Use Formula 9 to find the curvature. pasta quintoon 17. r(t) = (t, 3 cos t, 3 sin t) (a) Find the unit tangent and unit normal vectors T(t) and N(t). WA from the point (1, 0) Ess th 18. r(t) = (t², sin t - t cost, cost + t sin t), t> 0 19. r(t) =(√2t, e', e')) or the graph of kin 20. r(t) = (1, 1², 1²) loups bril (39MAX3 21-23 Use Theorem 10 to find the curvature. 21. r(t) = t³j + t² k le our by 22. r(t) = ti + t²j+e'k 23. r(t) = √√√6t² i + 2t j + 2t³ k 24. Find the curvature of r(t) = (t², In t, t ln t ) at the 5 Find the one I 25. Find the curvature of r(t) = (t, t², t³) at the point (1, 1, 1). and Ba 26. Graph the curve with parametric equations x == cos t, y = sin t, z = sin 5t and find the curvature at the point (1, 0, 0). vectors that are orthogonal od) bus ziləri adi awoda & brugt signiaza hi suala guideluso is orthogonal to 1). Note (740 can define algmat foc 27-29 Use Formula 11 to find the curvature. 27. y = x4 28. y = tan x LM 30. y = ln x Alummo1 si 5190 st Jornal veel The binonnal vector is the circular helix 30-31 At what point does the curve have maximum curvature? What happens to the curvature as x → ∞o? 102 OIT 8 BAUDA YA 29. y = xe* 01015 Stoporli Joups origin. 32. Find an equation of a parabola that has curvature 4 at the (19 guitsluoeo 33. (a) Is the curvature of the curve C shown in the figure greater at P or at Q? Explain. (b) Estimate the curvature at P and at Q by sketching the osculating circles at those points. 31. y = e* alorio e BAUDA slodining sdi bus storio sibi tarti sobo/ Ping CLAS sogge C CA C
Transcribed Image Text:A to sasiq yd boninnatab onslq sT T 17-20 srl mon estos smen od t≤ 5 q art gainianos niainos tadi sasia sib to sasly griminos0 t≤ 1 bidw browe!) 2017 0 < t < π/4 bolts *3 <4 ap to four decimal places. gral.) 4900 (1, 0, 0) to (1, 4, 0) ations x = sin t, length of this curve the parabolic cylinder nd the exact length of C 5). the length of the curve 2 y² = 4 and the plane or the curve measured sing t and then c length starting from curve (in the direction P(4, 1, 3) K, k, P(0, 1,√√2) = ) and move 5 units 2t 1² + 1 3 cost in the posi- j istros is onsl point (1, 0, 0). 2006 JOH (b) Use Formula 9 to find the curvature. pasta quintoon 17. r(t) = (t, 3 cos t, 3 sin t) (a) Find the unit tangent and unit normal vectors T(t) and N(t). WA from the point (1, 0) Ess th 18. r(t) = (t², sin t - t cost, cost + t sin t), t> 0 19. r(t) =(√2t, e', e')) or the graph of kin 20. r(t) = (1, 1², 1²) loups bril (39MAX3 21-23 Use Theorem 10 to find the curvature. 21. r(t) = t³j + t² k le our by 22. r(t) = ti + t²j+e'k 23. r(t) = √√√6t² i + 2t j + 2t³ k 24. Find the curvature of r(t) = (t², In t, t ln t ) at the 5 Find the one I 25. Find the curvature of r(t) = (t, t², t³) at the point (1, 1, 1). and Ba 26. Graph the curve with parametric equations x == cos t, y = sin t, z = sin 5t and find the curvature at the point (1, 0, 0). vectors that are orthogonal od) bus ziləri adi awoda & brugt signiaza hi suala guideluso is orthogonal to 1). Note (740 can define algmat foc 27-29 Use Formula 11 to find the curvature. 27. y = x4 28. y = tan x LM 30. y = ln x Alummo1 si 5190 st Jornal veel The binonnal vector is the circular helix 30-31 At what point does the curve have maximum curvature? What happens to the curvature as x → ∞o? 102 OIT 8 BAUDA YA 29. y = xe* 01015 Stoporli Joups origin. 32. Find an equation of a parabola that has curvature 4 at the (19 guitsluoeo 33. (a) Is the curvature of the curve C shown in the figure greater at P or at Q? Explain. (b) Estimate the curvature at P and at Q by sketching the osculating circles at those points. 31. y = e* alorio e BAUDA slodining sdi bus storio sibi tarti sobo/ Ping CLAS sogge C CA C
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