Recent content by jens.w

Yea that makes sense. That also makes sense! And how creative too. Your right, i was confused. I guess the problem i had (besides being stupid of course) is that i got hung up on the results from the definition. They seemed to conflict and give 2 different cases, but that wasnt the...

Yes, i thought of that at first, but it doesn't help in this case since x_{n}-L can be either positive or negative at all points, or alternating, depending on what series x_{n} is a part of. So based on that, i can't exclude one of the cases via the definition.

Homework Statement Given that \epsilon> 0, why is it, that \left | x_{n} -L\right |< \epsilon implicates that x_{n} > L-\epsilon ? Homework Equations The Attempt at a Solution

Yes, yes, yes. Nytik you made it much clearer. Especially with the example. Also thank you HallsofIvy. Now it actually makes sense to put those demands on the sequence, to be comfortable with saying that it will approach a limit. Thank you!

Homework Statement I'm having an enormously hard time wrapping my head around the following definition, which is using some concepts that keep showing up in other definitions and theorems. I'll state the definition and then i'll ask about the parts that i don't understand: We say that...

Thank you very much Mark44, SammyS, HallsofIvy, gb7nash and Dick.

Ok, since x^{3}+x > 0 when 0 < x < 1 and since x^{3}+x \rightarrow 0 when x \rightarrow 0 we should get \lim_{x\rightarrow 0+}f(x^{3}+x) = A Am i right?

Oh right, that's how compositions are structured! Darn i have forgotten alot. Ok, so since we have x^3 - x in place of x, in the original function f(x), and x^3 - x < 0 when 0 < x < 1, we have created the situation \lim_{x\rightarrow 0-}f(x) Wich is B. The answer is B. Did i...

Am i wrong in assuming that if for instance f(x)=Ax+B then f(x^{3}-x)=(Ax+B)^{3}-(Ax+B) ?

Oh ok, darn. I just tested it with f(x) = Ax + B, which was stupid. I was trying to find a theorem about it in my textbook (Calculus by Adams) but failed. Any tips on books that can teach me more about composite functions? Negative, since x3 < x there.

Homework Statement If \lim_{x\rightarrow 0+}f(x)=A and \lim_{x\rightarrow 0-}f(x)=B find \lim_{x\rightarrow 0+}f(x^{3}-x) Homework Equations The Attempt at a Solution I don't have one. I am dumbfounded. Mostly i have been trying to understand the meaning of the composite...