Lesson#27HW Name______________________________Per________

DifferentialsandLinearization

Findthedifferentialofeach:1. 𝑔 𝑥 = 𝑡𝑎𝑛𝑥

2. ℎ 𝑥 = 𝑥! − 3𝑥! + 4𝑥

3. 𝑘 𝑥 = csc 5𝑥 4. 𝑝 𝑥 = !

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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.