At the beginning of this week, I was really confident I understood limits. On Wednesday, though, I got a little worried about one question on the quiz over limits. The last question was a little difficult for me and I have no idea how I did with it. The problem was similar to this:
a. f(x)=ln(13x)
What is the limit of f(x) as x approaches ∞?
b. g(x)-ln(x-5)
What is the limit of g(x) as x approaches ∞?
c. What is the limit of (f+g)(x) as x approaches ∞?
d. Why does this break the sum/difference rule of limits?
The first three parts were pretty simple because I was able to just plug in a number and then confirm my answer by looking at a graph, but the last part was more difficult. I really didn't know how to answer the question, so I just answered it with what I thought made the most sense. . .
Continuity is our new topic that we learned about on Friday. At first I really struggled with the fact that a graph that looks like this. . .
can be considered continuous and discontinuous, depending on how you're asked to look at the graph. This function looks like it has infinite discontinuity, but it can be considered as continuous because the definition of a continuous function is "one that is continuous at every pint IN THE DOMAIN." So, this function is continuous because the domain is (-∞, 1) , (1, ∞) , and doesn't include one where the graph would be discontinuous.
a. f(x)=ln(13x)
What is the limit of f(x) as x approaches ∞?
b. g(x)-ln(x-5)
What is the limit of g(x) as x approaches ∞?
c. What is the limit of (f+g)(x) as x approaches ∞?
d. Why does this break the sum/difference rule of limits?
The first three parts were pretty simple because I was able to just plug in a number and then confirm my answer by looking at a graph, but the last part was more difficult. I really didn't know how to answer the question, so I just answered it with what I thought made the most sense. . .
Continuity is our new topic that we learned about on Friday. At first I really struggled with the fact that a graph that looks like this. . .
can be considered continuous and discontinuous, depending on how you're asked to look at the graph. This function looks like it has infinite discontinuity, but it can be considered as continuous because the definition of a continuous function is "one that is continuous at every pint IN THE DOMAIN." So, this function is continuous because the domain is (-∞, 1) , (1, ∞) , and doesn't include one where the graph would be discontinuous.