8 Matching Annotations
 Aug 2019

tutorial.math.lamar.edu tutorial.math.lamar.edu

So, the exponent goes to infinity in the limit and so the exponential must also go to infinity.
Will graphing the limit be an easier way to find whether the infinity is positive or negative?

Note as well, that in the last section the value of the limit did not depend on whether we went to plus or minus infinity
Why does the plus or minus affect these limits but not the ones in the section before?


tutorial.math.lamar.edu tutorial.math.lamar.edu

since the denominator is also not zero the fraction, and hence the limit, will be zero.
Will this occur for all similar set ups?


tutorial.math.lamar.edu tutorial.math.lamar.edu

(−4)f(−4)f(  4) doesn’t exist. There is no closed dot for this value of xxx and so the function doesn’t exist at this point
What does the open point mean or why is it places in the graph?


tutorial.math.lamar.edu tutorial.math.lamar.edu

Finally, we saw in the fourth example that the only way to deal with the limit was to graph the function. Sometimes this is the only way, however this example also illustrated the drawback of using graphs. In order to use a graph to guess the value of the limit you need to be able to actually sketch the graph. For many functions this is not that easy to do.
How do we know when we will need to graph the equation to find the limit.

f(x)−L
Do we always use L to solve for x?


tutorial.math.lamar.edu tutorial.math.lamar.edu

f(x)−f(a)x−a
the formula used to find the average rate of changes.


tutorial.math.lamar.edu tutorial.math.lamar.edu

The Definition of the Limit – In this section we will give a precise definition of several of the limits covered in this section. We will work several basic examples illustrating how to use this precise definition to compute a limit. We’ll also give a precise definition of continuity.
Will we have to memorize all of the types of limits and the properties to determining them?
