1310-Notes-Sec-52-filled - Math 1310 Section 5.2 The...

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Math 1310 Section 5.2 The Natural Exponential Function Although we don’t usually use a calculator in the course, we’ll need one to get started in this section. We want to see what happens to the expression n n + 1 1 as we let the number n get bigger and bigger. n n n + 1 1 10 100 1000 10,000 100,000 1,000,000 This is a mathematical idea called a limit, and you will learn more about limits if you take Math 1314 or Math 1431. What we can see is that as we let n get bigger and bigger, n n + 1 1 seems to be getting closer and closer to a specific irrational number. From our table, we can see that, to 5 decimal places, this number is 2.71828. We call this number e , and it is very important in all of mathematics. Since 1 e , e can be the base of an exponential function. So everything we learned in section 5.1 about graphing exponential functions will apply to graphing the function x e x f = ) ( . The graph of x e x f = ) ( will have the following features: Domain: ( - , Range: ( , 0 Key point: (0, 1) Horizontal asymptote: 0 = y since 0 y as -∞
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