Practice Euler's Number in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Euler's number e \approx 2.71828 is the unique base for which the exponential function e^x is its own derivative — the natural base for growth and decay.
The 'natural' base for growth—what you get from continuous compounding.
Example 1
easyEvaluate \lim_{n \to \infty}\left(1 + \frac{1}{n}\right)^n and state what this limit defines.
Example 2
hardShow that the derivative of f(x) = e^x is itself, i.e., f'(x) = e^x, using the limit definition of the derivative.
Example 3
easyUsing a calculator, compute e^2 to four decimal places. Then determine whether e^2 > 7.
Example 4
mediumA bank offers continuous compounding at an annual rate of 5\%. Using A = Pe^{rt}, find how much \1000 grows to after 10$ years.