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brunokabahizi
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Homework Statement
If the lim_{x→b} f(x)=c, then lim_{x→b} e^{x}= e^{c}. What property of the function g(x)=e^{x} allows this fact?
The Attempt at a Solution
Is it just because e is a constant?
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The constant e, also known as Euler's number, is a mathematical constant approximately equal to 2.71828. It is a fundamental constant in mathematics and has many important applications in calculus, exponential functions, and complex analysis.
The constant e was first introduced by the Swiss mathematician Leonhard Euler in the 18th century. It arises naturally in the study of compound interest and continuously compounded growth.
The constant e has several important properties, including being the base of the natural logarithm function, being the unique number with the property that its derivative is equal to itself, and being the limit of (1 + 1/n)^n as n approaches infinity.
The constant e is used extensively in mathematics, particularly in calculus and complex analysis. It is used to model continuous growth and decay, and to simplify calculations involving exponential and logarithmic functions.
The constant e has many real-life applications, including in finance, biology, physics, and engineering. It is used to model population growth, radioactive decay, and the spread of infectious diseases. It is also used in the calculation of interest and compound interest in financial transactions.