Study Guides

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: McGrawHill 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: McGrawHill 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: McGrawHill 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: McGrawHill 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: McGrawHill 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: McGrawHill Professional 
57.
Transcendental Functions Practice Test
Review the following concepts if needed: Logarithm Basics Help Derivative of Logarithm ...
Source: McGrawHill 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: McGrawHill 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: McGrawHill 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: McGrawHill Professional