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Limits At Infinity, Part II : In this section we desire to take a look at some other kinds of functions that frequently show up in limits at infinity. The functions we'll be discussed at here are natural logarithms, exponentials, and inverse tangents.
Let's begin by taking a look at some of very basic examples involving exponential functions.
Example: Evaluate following limits.
Solution
The major point of this example was to point out that if the exponent of an exponential goes towards infinity in the limit then the exponential function will also go towards infinity in the limit. Similarly, if the exponent goes to minus infinity in the limit then the exponential will go to zero in the limit.
Explain Graphing Equations with a Negative Slope? If the slope is a negative fraction, place the negative sign on either the numerator or the denominator. Example graph y = -2/
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Reduction -when the original amount and the balance or remainder are known, to find the part that has been given away. (e.g., there were 15 toffees in a container, and there are
Average cost function : Now let's turn our attention to the average cost function. If C ( x ) is the cost function for some of the item then the average cost function is,
What is a rational number?
In a polygon no 3 diagnols are concurrent. If the total no of points of intersection are 70 ( interior ). find the no. of diagnols? Ans) Since no 3 diagonals are concurrent, There
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three times the first of the three consecutive odd integers is 3 more than twice the third integer. find the third integer.
Product Rule: (f g)′ = f ′ g + f g′ As with above the Power Rule, so the Product Rule can be proved either through using the definition of the derivative or this can be proved
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