8 Due to programmimg constrain, answer keys will show decimal approximations, however give exactanswers whenever possible.For the curve defined byF(t) = (e cos(t), e' sin(t))find the unit tangent vector, unit normal vector, normal acceleration, and tangential acceleration atTt=2T(1/2)N()aT=16 12K|2k|2aN=> Next Question1 76 F

Answered: Image /qna-images/answer/57beaefa-0ef5-4643-b3ce-be849735b4d5.jpg

Answered: Due to programmimg constrain, answer…

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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Question

Due to programmimg constrain, answer keys will show decimal approximations, however give exact
answers whenever possible.
For the curve defined by
F(t) = (e cos(t), e' sin(t))
find the unit tangent vector, unit normal vector, normal acceleration, and tangential acceleration at
T
t=
2
T(1/2)
N()
aT=
16 12
K|2k|2
aN=
> Next Question
1 76 F

Expert Solution

Step 1: Evaluation of unit tangent vector:

$T with rightwards arrow on top open parentheses straight pi over 2 close parentheses equals open angle brackets negative fraction numerator 1 over denominator square root of e to the power of 2 straight pi end exponent plus 1 end root end fraction comma fraction numerator e to the power of straight pi over denominator square root of e to the power of 2 straight pi end exponent plus 1 end root end fraction close angle brackets$