Study Guides

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: McGrawHill 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: McGrawHill Professional 
3.
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: McGrawHill 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: McGrawHill 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: McGrawHill 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: McGrawHill Professional 
Source: McGrawHill Professional

8.
The Product and Quotient Rules Study Guide
The Product Rule When a function consists of parts that are added together, it is easy to take its derivative: Simply take the derivative of each part and add them together. We are inclined to try the same trick when the parts are multiplied together, but it does ...
Source: LearningExpress, LLC 
9.
Calculus and Chain Rule Study Guide
Calculus and Chain Rule We have found how to take derivatives of functions that are added, subtracted, multiplied, and divided. Next, we will cover how to work with a function that is put inside another simply by composition. For example, it would be ...
Source: LearningExpress, LLC 
10.
Differentiate Both Sides of the Equation Study Guide
Differentiate Both Sides of the Equation Once you have gotten the hang of implicit differentiation, it should not be difficult to take the derivative of both sides with respect to the variable t. This enables us to see how x and y vary ...
Source: LearningExpress, LLC

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