Study Guides

41.
Principles of Work Help
Introduction to Principles of Work One of the basic principles of physics is that work performed is force times distance: If you apply force F pounds in moving an object d feet, then the work is
Source: McGrawHill Professional 
42.
Averages Help
Introduction to Averages In ordinary conversation, when we average a collection p 1,..., pk of k numbers, we add them together and divide by the number of items:
Source: McGrawHill Professional 
43.
Arc Length and Surface Area Help
Introduction Arc Length and Surface Area Just as the integral may be used to calculate planar area and spatial volume, so this tool may also be used to calculate the arc length of a curve and surface area. The basic idea is to approximate the length of a curve by ...
Source: McGrawHill Professional 
44.
Hydrostatic Pressure Help
Introduction to Hydrostatic Pressure If a liquid sits in a tank, then it exerts force on the side of the tank. This force is caused by gravity, and the greater the depth of the liquid then the greater the force. Pascal’s principle asserts that the ...
Source: McGrawHill Professional 
45.
The Trapezoid Rule Help
Introduction to The Trapezoid Rule While there are many integrals that we can calculate explicitly, there are many others that we cannot. For example, it is impossible to evaluate
Source: McGrawHill Professional 
46.
Applications of the Integral Practice Test
Review the following concepts if needed: Volumes by Slicing Help
Source: McGrawHill Professional 
47.
Graphs of Functions Help
Introduction to Graphs of Functions It is useful to be able to draw pictures which represent functions. These pictures, or graphs , are a device for helping us to think about functions. In this book we will only graph functions whose domains and ranges ...
Source: McGrawHill Professional 
48.
Plotting the Graph of a Function Help
Introduction to Plotting the Graph of a Function Until we learn some more sophisticated techniques, the basic method that we shall use for graphing functions is to plot points and then to connect them in a plausible manner.
Source: McGrawHill Professional 
49.
Composition of Functions Help
Introduction to Composition of Functions Suppose that f and g are functions and that the domain of g contains the range of f . This means that if x is in the domain of f then f ( x ) makes ...
Source: McGrawHill Professional 
50.
The Inverse of a Function Help
Introduction to The Inverse of a Function Let f be the function which assigns to each working adult American his or her Social Security Number (a 9digit string of integers). Let g be the function which assigns to each ...
Source: McGrawHill Professional