Study Guides
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71.
Trigonometric Values of Angles Study Guide
Trigonometric Values of Angles Some very interesting and important functions are formed by dividing the length of one side of a right triangle by the length of another side. These functions are called trigonometric because they come from the geometry of a ...
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72.
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 ...
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73.
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 ...
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74.
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 ...
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75.
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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76.
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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77.
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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78.
Implicit Differentiation Study Guide
Implicit Differentiation A common complaint about the Chain Rule is "I don't know where to stop!" For example, why do we use the Chain Rule for f(x) = sin(x3) to get f'(x) = ...
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79.
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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80.
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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