Math Study Guides

Get help with math by selecting the topic below that you're interested in learning more about. From pre-algebra to calculus we've got study materials to help you learn.

Study Guides

showing 51 - 60 of 1014
  • 51.

    Derivative of Logarithm Function Help

    The Logarithm Function and the Derivative Now you will see why our new definition of logarithm is so convenient. If we want to differentiate the logarithm function we can apply the Fundamental Theorem of Calculus:

    Source: McGraw-Hill Professional
  • 52.

    Exponential Basics Help

    Exponential Basics Examine Fig. 6.4, which shows the graph of the function f(x) = ln x, x > 0.

    Source: McGraw-Hill Professional
  • 53.

    Exponentials with Arbitrary Bases Help

    Introduction to Exponentials with Arbitrary Bases We know how to define integer powers of real numbers. For instance

    Source: McGraw-Hill Professional
  • 54.

    Derivative and Integral of Logarithm Help

    Introduction to Derivative and Integral of Logarithm We begin by noting these facts: If a > 0 then

    Source: McGraw-Hill Professional
  • 55.

    Exponential Growth and Decay Help

    Introduction to Exponential Growth and Decay Many processes of nature and many mathematical applications involve logarithmic and exponential functions. For example, if we examine a population of bacteria, we notice that the rate at which the population grows is ...

    Source: McGraw-Hill Professional
  • 56.

    Inverse Trigonometric Functions Help

    Introduction to Inverse Trigonometric Functions Figure 6.14 shows the graphs of each of the six trigonometric functions. Notice that each graph has the property that some horizontal line intersects the graph at least twice. Therefore none of these functions is ...

    Source: McGraw-Hill Professional
  • 57.

    Transcendental Functions Practice Test

    Review the following concepts if needed: Logarithm Basics Help Derivative of Logarithm ...

    Source: McGraw-Hill Professional
  • 58.

    Integration by Parts Help

    Introduction to Integration by Parts We know that the integral of the sum of two functions is the sum of the respective integrals. But what of the integral of a product? The following reasoning is incorrect:

    Source: McGraw-Hill Professional
  • 59.

    Partial Fractions Help

    Introduction to Partial Fractions The method of partial fractions is used to integrate rational functions, or quotients of polynomials. We shall treat here some of the basic aspects of the technique. The first fundamental ...

    Source: McGraw-Hill Professional
  • 60.

    Methods of Integration - Substitution Help

    Introduction to Methods of Integration - Substitution Sometimes it is convenient to transform a given integral into another one by means of a change of variable. This method is often called “the method of change of variable” or “ u ...

    Source: McGraw-Hill Professional

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