5_4_exponential_functions

5_4_exponential_functions - 5.4 Exponential Functions...

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Unformatted text preview: 5.4 Exponential Functions: Differentiation and Integration Assignment: 5.4 # 115, 2528 all, 29, 37, 39 41, 45, 49, 51, 53, 57, 6339, 73, 79 99, 103, 107, 111, 115, 117, 121 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 1 5.4 Exponential Functions: Differentiation and Integration Consider a single cell bacteria: Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 2 Exponential Function This is base 2. Have you seen functions with a different base? Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 3 5.4 Exponential Functions: Differentiation and Integration Natural Exponential Function y = ln x Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 4 Properties of the Natural Exponential Function y = e x Domain? Range? y = e x Continuous? y = e x 1to1? Concave up or down? Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 5 5.4 Exponential Functions: Differentiation and Integration Solving equations with variable exponents Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 6 5.4 Exponential Functions: Differentiation and Integration Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 7 5.4 Exponential Functions: Differentiation and Integration The log is the exponent. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 8 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 9 5.4 Exponential Functions: Differentiation and Integration Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 10 5.4 Exponential Functions: Differentiation and Integration Finding the derivative...... ? Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 11 5.4 Exponential Functions: Differentiation and Integration Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 12 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 13 5.4 Exponential Functions: Differentiation and Integration Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 14 5.4 Exponential Functions: Differentiation and Integration Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 15 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 16 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 17 5.4 Exponential Functions: Differentiation and Integration Example of Exponential Function used in Statistics Standard Normal Probability Density Function has mean of 0 and Inflection point at + 1 Find the inflection points if =1 (See textbook to check your solution) Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 18 5.4 Exponential Functions: Differentiation and Integration Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 19 5.4 Exponential Functions: Differentiation and Integration Homework Part 2 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 G. Battaly, 2011 20 5.4 Exponential Functions: Differentiation and Integration Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 21 ...
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This note was uploaded on 09/09/2011 for the course MATH 1431 taught by Professor Any during the Fall '08 term at University of Houston.

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