Consider the following vector function. r(t) = (3/Zt, e3t, e-3t) (a) Find the unit tangent and unit normal vectors T(t) and N(t). (3V2,3e3f, – 3e-3t T(t) | V 18 + 9e5t + 9e¯6? N(t) (b) Use this formula to find the curvature. K(t) :

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the following vector function.
r(t) = (3/2t, e3t, e-3ty
(a) Find the unit tangent and unit normal vectors T(t) and N(t).
(3v7,3e,
-3t
- 3e
T(t)
%D
V 18 + 9eo7 + 9e-6t
N(t)
(b) Use this formula to find the curvature.
K(t) =
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Transcribed Image Text:Consider the following vector function. r(t) = (3/2t, e3t, e-3ty (a) Find the unit tangent and unit normal vectors T(t) and N(t). (3v7,3e, -3t - 3e T(t) %D V 18 + 9eo7 + 9e-6t N(t) (b) Use this formula to find the curvature. K(t) = Need Help? Read It
Use polar coordinates to find the limit. [If (r, 0) are polar coordinates of the point (x, y) with r 2 0, note that r →
of as (x, y) –→ (0, 0).] (If an answer does not exist,
enter DNE.)
lim
(x² + y?) In(x² + y²)
(x, y) → (0, 0)
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Transcribed Image Text:Use polar coordinates to find the limit. [If (r, 0) are polar coordinates of the point (x, y) with r 2 0, note that r → of as (x, y) –→ (0, 0).] (If an answer does not exist, enter DNE.) lim (x² + y?) In(x² + y²) (x, y) → (0, 0) Need Help? Read It
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