Limits are now still a little confusing.
1. Like I still cant get the idea of limits that are continoious. I taught I knew which limits are still continuous but then the numbers came to play like the amplitude and the ranges are still messing me up. Then also the "hole" in the lines also messes me up. So how can I can I know how it is continuous or not?
2. Another thing is onndetermining the limit and to find out if there is one or not. Like the one in the test lim x->2+ then there are three points lined up in 2 so that throws me off a little.
3. Then the limits with the end behavior and then graphing them confuse me. When there is a fraction and then find the end behavior model for it and then graph it. For me it's all confusing because I don't know how to graph it.
So please help!
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1. Continuity and limits are not to be confused. Limits are looking for what the OUTPUTS are approaching as the INPUT approaches a number.
ReplyDeleteContinuity involve using limits to see if a function is continuous, but limits are not considered "continuous or not continuous," only FUNCTIONS are considered continuous or not continuous.
If you can't plug in a number for x because of a domain issue, then there is probably a hole or an asymptote there. If you can simplify the problem to make that domain issue go away, then it's a hole. If you cannot simplify, then it's a vert. asymptote.
2. Remember, limits are looking for what the OUTPUTS are APPROACHING as that input creeps closer and closer to 2. It does not care about what actually happens AT x=2.