- #1
weirdobomb
- 15
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Homework Statement
Would you give me a clue as to how, limit as z approaches infinity,
[[1 + (1/z)]^z]^(1/3) = e^(1/3)
The number e is a mathematical constant that is approximately equal to 2.71828. It is the base of natural logarithms and is used to represent exponential growth and decay in many scientific and mathematical equations.
The formula for e^x is e raised to the power of x, which can also be written as exp(x). This means that e is multiplied by itself x times, resulting in an exponential growth or decay depending on the value of x.
The graph of e^x is a smooth, continuous curve that starts at the point (0,1) and increases rapidly as x increases. It has a horizontal asymptote at y=0, meaning that the curve will never touch or cross the x-axis.
e^x is important in calculus because it is the only function that is equal to its own derivative. This property makes it a useful tool for solving differential equations and understanding rates of change in continuous systems.
e^x is used in many real-life applications, such as compound interest calculations, population growth models, and radioactive decay equations. It also has applications in physics, chemistry, and biology to describe natural phenomena and predict future outcomes.