Section 5.1 B - Students' Notes

# Section 5.1 B - Students' Notes - Section 5.1B THE NATURAL...

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Section 5.1B THE NATURAL LOGARITHMIC FUNCTION: DIFFERENTIATION THE NATURAL LOGARITHMIC FUNCTION: DIFFERENTIATION Objectives Objectives : 1) Develop and use properties of the natural logarithmic function 2) Understand the definition of the number e 3) Find derivatives of functions involving the natural logarithmic function Procedures Procedures : Check homework – Collect it Check homework – Collect it y t y 1 = I. Definition Definition : 0 1 1 = x , dt t x ln x 1 x x Example 1 : Estimate the area of the function 2 1 , 1 = x x y with 4 = n Area = lnx y 1 1 2 x Solve : Area (left) 7595 . 0 Area (right) 6345 . 0 Area (Simpson’s Rule) 69325 . 0 Area (Trapezoidal Rule) 6970 . 0 6931 . 0 2 ln 1 ln 2 1 = = dt t x II. The Number The Number e ( 718281828 . 2 e ) Definition of e : 1 1 ln 1 = = e dt t e Example 2 : Evaluate a) 2 ln e Solve : 1

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_______________________________________________________________________________________ b) 3 1 ln e
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Section 5.1 B - Students' Notes - Section 5.1B THE NATURAL...

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