Study Guides

1.
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 
2.
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 
3.
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 
4.
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 
5.
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 
6.
Transcendental Functions Practice Test
Review the following concepts if needed: Logarithm Basics Help Derivative of Logarithm ...
Source: McGrawHill Professional 
7.
Logarithms with Arbitrary Bases Help
Introduction to Logarithms with Arbitrary Bases If you review the first few paragraphs of Section 1, you will find an intuitively appealing definition of the logarithm to the base 2: log
Source: McGrawHill Professional 
8.
Logarithm and Exponential Graphing Help
Logarithm and Exponential Graphing If a > 0 and f(x) = log a x, x > 0, then
Source: McGrawHill Professional 
9.
Logarithmics Differentiation Help
Logarithmics Differentiation We next show how to use the logarithm as an aid to differentiation. The key idea is that if F is a function taking positive values then we can exploit the formula
Source: McGrawHill Professional 
10.
Radioactive Decay Help
Introduction to Radioactive Decay Another natural phenomenon which fits into exponential growth and decay is radioactive decay . Radioactive material, such as C 14 (radioactive carbon), has a ...
Source: McGrawHill Professional

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