To this point we’ve been able to “reuse” work from the first limit in the at least a portion of the second limit.
It’s interesting to see the same identical problem come out with different results depending if the infinity is negative or positive
9 Matching Annotations
- Aug 2019
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tutorial.math.lamar.edu tutorial.math.lamar.edu
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if the argument goes to infinity then the log also goes to infinity in the limit.
doing this section of the practice problems proved to be a fun challenge.
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tutorial.math.lamar.edu tutorial.math.lamar.edu
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We won’t need these facts much over the next couple of sections but they will be required on occasion
Nonetheless, they should be thought as an important method of mathematics.
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limit didn’t change the answer
would it have something to do with the infinite sign being +/-?
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tutorial.math.lamar.edu tutorial.math.lamar.edu
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The only difference this time is that the function only needs to settle down to a single number on either the right side of x=ax=ax = a or the left side of x=ax=ax = a depending on the one‑sided limit we’re dealing with.
this is an interesting and helpful way to make ‘guessing’ a number to be applied into the function!
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tutorial.math.lamar.edu tutorial.math.lamar.edu
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The limit is only concerned with what is going on around the point x=a
Knowing what’s going on around the x value, is like drawing a detailed scenery without actually having a centerpiece to focus on. We’re trying to understand what’s going on AROUND the x value, before looking at x, directly.
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tutorial.math.lamar.edu tutorial.math.lamar.edu
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Last, we were after something that was happening at x=1x=1x = 1 and we couldn’t actually plug x=1x=1x = 1 into our formula for the slope. Despite this limitation we were able to determine some information about what was happening at x=1x=1x = 1 simply by looking at what was happening around x=1x=1x = 1. This is more important than you might at first realize and we will be discussing this point in detail in later sections.
This reminds me of the exercise we had this morning in class.
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Likewise, at the second point shown, the line does just touch the graph at that point, but it is not “parallel” to the graph at that point and so it’s not a tangent line to the graph at that point.
A visual representation of a Tangent Line is very useful, I honestly wasn’t visualizing what a Tangent Line was, in my head.
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tutorial.math.lamar.edu tutorial.math.lamar.edu
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We will be seeing limits in a variety of places once we move out of this chapter.
Will the L’Hospital method be explained in this chapter?
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