6. Let C be the curve in R´ given by the vector-valued function r : R → R defined as r(t) = (cos(e – t), In(ln(t)), t', t2/3,0). (a) Determine whether the curve C passes through the point (1,0, eº, Ve?, 0). (b) Compute the tangent vector to C when t length.). Where is this curve differentiable? Give your answer in interval notation. = e (Note: This does not need to have unit (c) What is the domain of r?. The curve C belongs to a particular subset of Rº. What is this set? Explain. (Note: A basic element/point of R³ should have the form (*1, X2, T3, C4, Tz). For the subset question, think in terms of higher-dimensional "planes").
6. Let C be the curve in R´ given by the vector-valued function r : R → R defined as r(t) = (cos(e – t), In(ln(t)), t', t2/3,0). (a) Determine whether the curve C passes through the point (1,0, eº, Ve?, 0). (b) Compute the tangent vector to C when t length.). Where is this curve differentiable? Give your answer in interval notation. = e (Note: This does not need to have unit (c) What is the domain of r?. The curve C belongs to a particular subset of Rº. What is this set? Explain. (Note: A basic element/point of R³ should have the form (*1, X2, T3, C4, Tz). For the subset question, think in terms of higher-dimensional "planes").
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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Transcribed Image Text:6.
Let C be the curve in R´ given by the vector-valued function r : R → R³
defined as r(t) = (cos(e – t), In(In(t)), t', t213,0).
(a) Determine whether the curve C passes through the point (1,0, eº, Ve²,0).
(b) Compute the tangent vector to C when t = e (Note: This does not need to have unit
length.). Where is this curve differentiable? Give your answer in interval notation.
(c) What is the domain of r?. The curve C' belongs to a particular subset of R°. What
is this set? Explain. (Note: A basic element/point of R should have the form
(X'1, X2, X3, X4, X5). For the subset question, think in terms of higher-dimensional
"planes").
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