Study Guides

51.
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 
52.
Logarithm and Exponential Graphing Help
Logarithm and Exponential Graphing If a > 0 and f(x) = log a x, x > 0, then
Source: McGrawHill Professional 
53.
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 
54.
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 
55.
Compound Interest Help
Introduction Compound Interest Yet a third illustration of exponential growth is in the compounding of interest. If principal P is put in the bank at p percent simple interest per year then after one year the account has
Source: McGrawHill Professional 
56.
Other Inverse Trigonometric Functions Help
Introduction to Other Inverse Trigonometric Functions The most important inverse trigonometric functions are Sin −1, Cos −1, and Tan ...
Source: McGrawHill Professional 
57.
The Method of Cylindrical Shells Help
Introduction to The Method of Cylindrical Shells Our philosophy will now change. When we divide our region up into vertical strips, we will now rotate each strip about the y axis instead of the x axis. Thus, instead of generating a disk with ...
Source: McGrawHill Professional 
58.
Surface Area Help
Introduction to Surface Area Let f ( x ) be a nonnegative function on the interval [ a, b ]. Imagine rotating the graph of f about the x axis. This procedure will generate a surface of revolution, as shown in Fig. ...
Source: McGrawHill Professional 
59.
Simpson's Rule Help
Introduction to Simpson's Rule Simpson’s Rule takes our philosophy another step: If rectangles are good, and trapezoids better, then why not approximate by curves? In Simpson’s Rule, we approximate by parabolas.
Source: McGrawHill Professional 
60.
Derivative of Exponential Help
Calculus Properties of the Exponential Now we want to learn some “calculus properties” of our new function exp( x ). These are derived from the standard formula for the derivative of an inverse, as in Section 2.5.1. ...
Source: McGrawHill Professional