As the title says, how come the value e is special? it has functions and rules just dedicated to it, but what sets it apart from another random number?
In: 397
Look at the function: (1+(1/x))^x and think about what happens as x grows. The whole term will grow exponentially. However, (1/x) will get smaller and smaller until it is essentially 0. These growing and shrinking fight eachother as x grows, making it hard to determine what x will be. It turns out, that function converges to e as x approaches infinity. That is the definition of e, and is what makes it a special number. This is useful because that function is used to describe situations where things grow exponentially. (Lots of things grow exponentially, so it comes up often.)
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