Question

Also I'm just learning about limits. I''ve learned about indeterminate forms, but not sure how to tell if the limit actually DNE or I've just missed calculating it in indeterminate form?!?! For example....I can tell by the graph that the limit of (3x+7)/(x-5) (as x approaches 5) DNE from the graph, but how do I tell algebraically? Even though the graph DNE at x=5, does not necessarily mean the limit DNE....

Answer 1

Algebraically, you need to take the limit from both the right hand side and left hand side separately. That is to say, as the function approaches the point from the positive side, and from the negative side. If they do not approach the same value, then the limit does not exist. This is also a condition for continuity, which I imagine you'll learn later!

Answer 2

Right, I thought so, but then was wondering how....I have only done it with absolute value, which seems easier. Do I just plug in the left limit of say, 4.9, and a right limit of 5.1? or something similar? is that enough alegraic support?

Answer 3

that would seem not so reliable when dealing with exponential functions...would it? (when I get there of course)

Answer 4

easy method is to replace x by 5. if you get
\[\frac{a}{0}, a\neq 0\] then the limit does not exist. if you get
\[\frac{0}{0}\] then you have more work to do

Answer 5

No you would need to do more than just one number on each side. Since you seem like you're just starting out, I would do 10 for each side so you can visualize it more, and get a better feel for what the function is approaching.

Answer 6

oh, ok. so, an snswer of 0/0 indicates an indeterminate form? (possibly)

Answer 7

Yes

Answer 8

sweet! thanks