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Question. Suppose exists, find the limit: (1) (2) Sol. (1) (2) (1) Suppose exists and then

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  1. Question • Suppose exists, find the limit: (1) (2) Sol. (1) (2) • (1) Suppose exists and then (2) Suppose as then

  2. Question Suppose exists and find the limit The solution is Sol.

  3. Derivatives of logarithmic functions • The derivative of is • Putting a=e, we obtain

  4. Example Ex. Differentiate Sol. Ex. Differentiate Sol.

  5. Question Find if Sol. Since it follows that Thus for all

  6. Example Find if Sol. Since it follows that and by definition, Thus for all x

  7. Question Find if (a) (b) (c) Sol. (a) (b) (c)

  8. The number e as a limit • We have known that, if then • Thus, which by definition, means • Or, equivalently, we have the following important limit

  9. Other forms of the important limit • Putting u=1/x, we have • More generally, if then

  10. Question Suppose exists and find the limit The solution is Sol. Let then

  11. Question Discuss the differentiability of and find Sol. does not exist

  12. Homework 6 • Section 3.6: 46, 49, 50 • Section 3.7: 16, 20, 34, 35, 39, 40, 63 • Section 3.8: 41, 45, 48

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