Study Guides

31.
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: McGrawHill Professional 
32.
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: McGrawHill Professional 
33.
Transcendental Functions Practice Test
Review the following concepts if needed: Logarithm Basics Help Derivative of Logarithm ...
Source: McGrawHill Professional 
34.
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: McGrawHill Professional 
35.
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: McGrawHill Professional 
36.
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: McGrawHill Professional 
37.
Integrals of Trigonometric Expressions Help
Introduction to Integrals of Trigonometric Expressions Trigonometric expressions arise frequently in our work, especially as a result of substitutions. In this section we develop a few examples of trigonometric integrals. The ...
Source: McGrawHill Professional 
38.
Methods Of Integration Practice Test
Review the following concepts if needed: Integration by Parts Help
Source: McGrawHill Professional 
39.
Volumes by Slicing Help
Introduction to Volumes by Slicing When we learned the theory of the integral, we found that the basic idea was that one can calculate the area of an irregularly shaped region by subdividing the region into “rectangles.” We put the word ...
Source: McGrawHill Professional 
40.
Volumes of Solids of Revolution Help
Introduction to Volumes of Solids of Revolution A useful way—and one that we encounter frequently in everyday life—for generating solids is by revolving a planar region about an axis. For example, we can think of a ball (the interior of a sphere) as ...
Source: McGrawHill Professional