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MAT 1235 Calculus II

MAT 1235 Calculus II. Section 6.3* The Natural Exponential Functions. http://myhome.spu.edu/lauw. Homework and …. WebAssign HW 6.3* 33 problems -- most of them are straight forward Due Wednesday Be sure to start early. Preview. Recall. 6.1 6.2* . Definition (6.2*).

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MAT 1235 Calculus II

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  1. MAT 1235Calculus II Section 6.3* The Natural Exponential Functions http://myhome.spu.edu/lauw

  2. Homework and … • WebAssign HW 6.3* • 33 problems -- most of them are straight forward • Due Wednesday • Be sure to start early

  3. Preview

  4. Recall • 6.1 • 6.2*

  5. Definition (6.2*) • Let be the number such that

  6. Definition (6.2*) • Let be the number such that • ………

  7. Definition (Inverse of ) Let be the inverse function of In particular, we have

  8. Then,… , i.e. , i.e. , where is an rational number, we get

  9. Then,… , i.e. , i.e. , where is an rational number, we get

  10. So,… • and give the same values for rational numbers • However, is undefined for irrational number (not yet!)

  11. It makes sense to define…

  12. Properties

  13. Properties (limits at infinities)

  14. Properties (limits at infinities)

  15. Example 1 (a)

  16. Example 1 (a)

  17. Example 1 (b)

  18. Example 1 (c)

  19. Remarks • ∞ is not a number, it is a concept. • In particular, you should not write: • Again, you can blame whoever told you that this is ok. But it is your responsibility to do the right thing from now on.

  20. Derivatives & Antiderivatives

  21. Derivatives & Antiderivatives

  22. Example 2

  23. Example 3

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