Chapter 5 Logarithmic, Exponential, and Course Number Transcendental Functions Instructor Section 5.1 The Natural Logarithmic Function: Differentiation Date Objective: In this lesson you learned the properties of the natural logarithmic function and how to find the derivative of the natural logarithmic function. Important Vocabulary Define each term or concept. Natural logarithmic function The natural logarithmic function is defined by ln = x x 1/t > dt, x 0. 1 The letter denotes the positive real number such that e e e ln = 1/t = 1. e dt 1 The Natural Logarithmic Function (Pages If a and b are positive numbers and The domain of the natural logarithmic function is the set n is rational, then the of all positive real numbers . following properties are true: The value of ln is positive for > 1 and negative x x 1. ln (1) = 0 for 0 < < 1 . Moreover, ln (1) = 0 , x . because the upper and lower limits of integration are equal ln (ab) = ln + ln a when = 1 . x . b ln(an) = ln n a The natural logarithmic function has the following properties: . The domain is (0, and the range is What you should learn How to develop and use The function is continuous, increasing, and one-to-one. properties of the natural logarithmic function The graph is concave downward. Larson/Edwards Calculus 9e Notetaking Guide IAE 95 Copyright © Cengage Learning. All rights reserved.
Chapter 5 Logarithmic, Exponential, and Transcendental Functions Section 5.1 The Natural Logarithmic Function: Differentiation Objective: In this lesson you learned the properties of the natural logarithmic function and how to find the derivative of the natural logarithmic function. Course Number Instructor Date Important Vocabulary Define each term or concept. Natural logarithmic function The natural logarithmic function is defined by ln x = x 1/t dt, x > 0. 1 e The letter e denotes the positive real number such that e ln e = 1/t dt = 1. 1 The Natural Logarithmic Function (Pages The domain of the natural logarithmic function is the set of all positive real numbers . The value of ln x is positive for x > 1 and negative for 0 < x < 1 . Moreover, ln (1) = 0 , because the upper and lower limits of integration are equal when x = 1 . The natural logarithmic function has the following properties: The domain is (0, and the range is The function is continuous, increasing, and one-to-one. The graph is concave downward. If a and b are positive numbers and n is rational, then the following properties are true: 1. ln (1) = 0 . ln (ab) = ln a + ln b . ln(an) = n ln a . What you should learn How to develop and use properties of the natural logarithmic function Larson/Edwards Calculus 9e Notetaking Guide IAE Copyright © Cengage Learning. All rights reserved. 95
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