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Introduction to Logarithms

"The importance of having inverse functions leads us to the introduction to logarithms as the inverses of exponential functions. Solving exponential equations often involves using the ideas presented ...

Important Limits

"An important limit in calculus, which is central to finding derivatives of exponential functions, involves finding the limit as h approaches 0 of a special function. This limit, one of a few importan ...

Graphing Logarithmic Functions

"In science classes we will often find ourselves graphing logarithmic functions to describe situations such as motion or speed over time. When trying to identify these situations as those seen in grap ...

Graphing Exponential Functions

"There are certain functions, such as exponential functions, that have many applications to the real world and have useful inverse functions. Graphing exponential functions is used frequently, we ofte ...

Solving Exponential Equations

"In the real world we often hear terms like exponential growth or exponential decay, when discussing solving exponential equations such as those used in compounding interest problems. In order to unde ...

Exponential Functions

"We often encounter exponential functions in science and mathematics. Exponential functions have a unique set of characteristics and asymptotic behavior that make their graphs recognizable. It is impo ...

Elementary Functions

"In math we often encounter certain elementary functions. These elementary functions include rational functions, exponential functions, basic polynomials, absolute values and the square root function. ...

Derivatives of Exponential Functions

"The derivative of an exponential function can be derived using the definition of the derivative. Derivatives of exponential functions involve the natural logarithm function, which itself is an impor ...

Properties of Logarithms

"In order to solve equations with logarithms and exponential functions, we must understand two properties of logarithms. These properties of logarithms are the methods we use to get to and solve for v ...

Continuous Functions

"In order for a function to have continuity at a certain point, several conditions including (1) the existence of the point in the domain and (2) the existence of a two-sided limit as the point approa ...

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