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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").

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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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").
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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