calc unit 3 lesson #27 hw - mrs. young's math...
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Lesson#27HW Name______________________________Per________
DifferentialsandLinearization
Findthedifferentialofeach:1. 𝑔 𝑥 = 𝑡𝑎𝑛𝑥
2. ℎ 𝑥 = 𝑥! − 3𝑥! + 4𝑥
3. 𝑘 𝑥 = csc 5𝑥 4. 𝑝 𝑥 = !
!!!
Usethelinearapproximationof𝒇 𝒙 at𝒙 = 𝒂toapproximatethevalueof𝒇(𝒃).
5. 𝑓 𝑥 = 5x!, 𝑎 = 3, 𝑏 = 3.1
6. 𝑓 𝑥 = 5x!, 𝑎 = 3, 𝑏 = 2.9
7. 𝑓 𝑥 = 𝑥, 𝑎 = 100, 𝑏 = 101
8. 𝑓 𝑥 = 𝑥! , 𝑎 = 16, 𝑏 = 17
Lesson#27HW Name______________________________Per________
9. 𝑓 𝑥 = 𝑥!/!, 𝑎 = 8, 𝑏 = 8.2
10. 𝑓 𝑥 = cos (𝑥), 𝑎 = 0, 𝑏 = 2°
11. 𝑓 𝑥 = sin (𝑥), 𝑎 = 0, 𝑏 = 2°Let𝒈(𝒙)bethelinetangenttothegraphof𝒇 𝒙 = 𝒙𝟑 − 𝟒𝒙+ 𝟏at𝒙 = 𝟏.
a) Writethefunction𝑔(𝑥).
b) Completethetable.
𝒙 𝒇(𝒙) 𝒈(𝒙)0.7 0.8 0.9 1 1.1 1.2 1.3
c) Describeanyobservationsthatyounoticeaboutthetableofvalues.
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