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Mth 173
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** Question Form_labelMessages **
Modeling Project 2 Question 14
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Modeling Project #2
Question #14
Use DERIVE to determine the approximate number n required to obtain the value 2.71828.
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I don't understand how to find n, when e is given as 2.71828
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e = limit{n -> infinity}( 1 + 1/n) ^ n.
e is an irrational number which is only approximately equal to 2.71828. It can be taken to as many decimal places as we wish. For example, to 30 significant figures the approximate value of e is 2.71828182845904523536028747135
We can approximate e by evaluating the expression in our definition for larger and larger values of n.
For example if n = 10, the expression (1 + 1/n)^2 is equal to about 2.5937. Not all that close to 2.718281828459 etc..
If n = 50 we get 2.6916.
If n = 10 000 we get 2.718145.
We're still not at the desired approximation 2.71828.
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