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1. r(t) = t²i- cos (8t) + sin (8t) k

1. r(t) = t²i- cos (8t) + sin (8t) k

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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For problems 1 - 3 find the unit tangent vector for the given vector function. 1. F(t) = ²7 cos (8t) 7 + sin (8t) k 2. r(t) = (8t, 2 t6, t¹) 3. r(t) = (In (6t), el-t,5t) For problems 4 & 5 find the tangent line to the vector function at the given point. 4. r(t) = (3+t², t¹, 6) at t = -1. 5. r(t) = (2t, cos² (t), e6t) at t = 0. For problems 6 & 7 find the unit normal and the binormal vectors for the given vector function. 6. r(t) = (et sin (t), e¹t cos (t), 2) 7. r(t) = 2ti+t² + In (1²) k
Transcribed Image Text:For problems 1 - 3 find the unit tangent vector for the given vector function. 1. F(t) = ²7 cos (8t) 7 + sin (8t) k 2. r(t) = (8t, 2 t6, t¹) 3. r(t) = (In (6t), el-t,5t) For problems 4 & 5 find the tangent line to the vector function at the given point. 4. r(t) = (3+t², t¹, 6) at t = -1. 5. r(t) = (2t, cos² (t), e6t) at t = 0. For problems 6 & 7 find the unit normal and the binormal vectors for the given vector function. 6. r(t) = (et sin (t), e¹t cos (t), 2) 7. r(t) = 2ti+t² + In (1²) k
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