For problems 1 - 3 find the unit tangent vector for the given vector function.1. F(t) = ²7 cos (8t) 7 + sin (8t) k2. 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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Answered: 1. r(t) = t²i- cos (8t) + sin (8t) k

Math

Geometry

1. r(t) = t²i- cos (8t) + sin (8t) k

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.5: Derivatives Of Logarithmic Functions

Problem 47E

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Question

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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