lect116_2_f11 - Thursday September 15 Lecture 2 Exponential...

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Thursday September 15 Lecture 2 : Exponential, logarithms and inverse functions (Refers to sections 1.6 to 1.8 in your text ) Students who have mastered the content of this lecture know about : Exponential functions , Euler’s number e , one-to-one function , inverse of a function , plotting the curve f 1 when the curve of f is known , the logarithm base a of x , the natural log , the log laws , the curve of a log function , the trig functions sine , cosine and tan and their curves, as well as their inverses, arcsine, arcos and arctan . 2.1 Definition An exponential function is a function of the form f ( x ) = a x where a is a positive constant. The number a is referred to as the base of the exponential function. Exponential functions satisfy the usual laws of exponents. 2.1.1 Example – Examples of exponential functions: y = 3 t , y = 2 t y = (1/2) x . 2.2 Definition – Suppose that f ( x ) = a x is an exponential function so that the slope of the tangent line to the curve of a x when x = 0 is 1.
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It can be shown that here is exactly one exponential function which satisfies this property. It is the one where the base is 2.71828… This is an irrational number which we will denote as e . It is called Euler’s number . The exponential function y = e x plays an important role in many areas of mathematics.
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This note was uploaded on 12/28/2011 for the course MATH 116 taught by Professor Robertandre during the Spring '11 term at Waterloo.

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lect116_2_f11 - Thursday September 15 Lecture 2 Exponential...

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