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4011 - Natural Logarithm Function

This resource provides a comprehensive overview of the natural logarithmic function (ln(x)), including its definition, properties, and integration rules. It explores key concepts such as the behavior of ln(x) at specific points, and includes graphical representations for better understanding. Examples of definite integrals and anti-derivatives involving ln are also presented, along with regression techniques using TI-83 calculators. This guide aims to enhance your understanding and application of logarithmic functions in calculus.

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4011 - Natural Logarithm Function

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  1. 4011- Natural Logarithm Function BC Calculus

  2. f(t) The Natural Logarithmic Function 0 .405 .693 .916 1.098

  3. f(t) The Natural Logarithmic Function -.223 -.511 -.916 -1.609

  4. f(t) H(x) The Natural Logarithmic Function

  5. Definition of ln (x) DEFN: The Natural Logarithmic Function is defined by Log Rule for Integration:

  6. L1 L2 1 0 1.5 .405 2 .693 2.5 .916 3 1.098 .8 -.223 .6 -.511 .4 -.916 .2 -1.609 STAT PLOT STAT ] EDIT 1: Edit ((fill the table)) [ 2nd ] ( Y= ) STAT PLOT 1: Plot 1 … On [ ZOOM ] 9: ZoomStat . . . . . . . . . . . . . . . [ Y = ] Y1 = ln (x) [ GRAPH]

  7. Integration EX:  EX: Definite Integrals

  8. TRIG Anti-derivatives involving ln Given without Proof:

  9. Last Update: • 02/1/10

  10. L1 L2 1 0 1.5 .405 2 .693 2.5 .916 3 1.098 .8 -.223 .6 -.511 .4 -.916 .2 -1.609 REGRESSION on the TI-83 STAT ] EDIT 1: Edit ((fill the table)) [ 2nd ] ( Y= ) STAT PLOT 1: Plot 1 … On [ ZOOM ] 9: ZoomStat . . . . . . . . . . . . . . . [ Y = ] Y1 = ln (x) [ GRAPH]

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