Study Guides
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1.
Calculus and the Idea of Limits Help
Introduction to Calculus and the Idea of Limits The single most important idea in calculus is the idea of limit. More than 2000 years ago, the ancient Greeks wrestled with the limit concept, and they did not succeed . It is only in ...
Source: McGraw-Hill Professional -
2.
Properties of Limits Help
Introduction to Properties of Limits To increase our facility in manipulating limits, we have certain arithmetical and functional rules about limits. Any of these may be verified using the rigorous definition of limit that was provided at the beginning of the last ...
Source: McGraw-Hill Professional -
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Continuity Help
Introduction to Continuity Let f be a function whose domain contains the interval (a, b). Assume that c is a point of (a, b). We say that the function f is continuous at c if
Source: McGraw-Hill Professional -
4.
The Derivative Help
Introduction to The Derivative Suppose that f is a function whose domain contains the interval (a , b). Let c be a point of (a , b). If the limit
Source: McGraw-Hill Professional -
5.
Rules for Calculating Derivatives Help
Introduction to Rules for Calculating Derivatives Calculus is a powerful tool, for much of the physical world that we wish to analyze is best understood in terms of rates of change. It becomes even more powerful when we can find some simple rules that enable us to ...
Source: McGraw-Hill Professional -
6.
The Derivative as a Rate of Change Help
Introduction to The Derivative as a Rate of Change If f(t) represents the position of a moving body, or the amount of a changing quantity, at time t , then the derivative f′(t) (equivalently, ( d/dt)f(t)) denotes the rate ...
Source: McGraw-Hill Professional -
Source: McGraw-Hill Professional
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8.
Calculus and Limits Study Guide
Calculus and Limits Mathematicians, just like children, like to see what happens when we push limits. We are told not to divide by zero, so the temptation overwhelms us to see what happens when we divide by almost zero. The process of using ...
Source: LearningExpress, LLC -
9.
Derivatives Study Guide
Derivatives Straight lines may be ideal to human beings, but most functions have curved graphs. This does not stop us from projecting straight lines on them! For example, at the point marked x on the graph in Figure 6.1, the function is clearly ...
Source: LearningExpress, LLC -
10.
Basic Rules of Differentiation Study Help
Basic Rules of Differentiation Using the limit definition to find derivatives can be very tedious. Luckily, there are many shortcuts available. For example, if function f is a constant, like f (x) = 5 or f ...
Source: LearningExpress, LLC
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