Study Guides

61.
Calculus Functions Study Guide
Introduction Calculus is the study of change. It is often important to know when something is increasing, when it is decreasing, and when it hits a high or low point. Much of the business of finance depends on predicting the high and low points for prices. In ...
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62.
Calculus Graphs Study Guide
Calculus Graphs A function can be fully described by showing what happens at each number in its domain (for example, 4→ 2) or by giving its formula (for example, f(x) = √x). ...
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63.
Exponents and Logarithms Study Guide
Exponents Because exponents form such an important part of calculus, we shall briefly review them. Generally, an means "multiply the base a as many times as the exponent n."
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64.
Rates of Change Study Guide
Rates of Change It is useful to contemplate slopes in practical situations. For example, suppose the following graph in Figure 8.1 is for y = f(x), a function that gives the price y for various amounts x of cheese. ...
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65.
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 ...
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66.
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 ...
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67.
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 ...
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68.
Limits at Infinity Study Guide
Limits at Infinity This lesson will serve as a preparation for the graphing in the next lesson. Here, we will work on ways to identify asymptotes from the formula of a rational function. Rational functions are quotients, with a clear numerator and ...
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69.
Graphs of Increasing and Decreasing Functions and Asymptotes Study Guide
Graphs of Increasing and Decreasing Functions and Asymptotes Here is where everything comes together. We know how to find the domain, how to identify asymptotes, and how to plot points. With the help of the sign diagrams from the previous lesson, we shall be able ...
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70.
Areas Under Curves Study Guide
Areas Under Curves Around the same time that so many great mathematicians devoted themselves to figuring out the slopes of tangent lines, other mathematicians were working on an entirely different problem. They wanted to be able to figure out the area underneath ...
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