Recent content by luke8ball

You mean so that I get: [lim f(ax) - f(0)]/x - [lim f(bx) - f(0)]/x x→0 x→0 I had thought about that, but I still don't see how that gives me af'(0) - bf'(0)...

I'm having trouble showing the following: lim [f(ax)-f(bx)]/x = f'(0)(a-b) x→0 I feel like this should be really easy, but am I missing something? I tried to use the definition of the derivative, but I know I can't just say f(ax)-f(bx) = (a-b)f(x). Any ideas?

I'm working on a problem where I need to show that the series of functions, f(x) = Ʃ (xn)/n2, where n≥1, converges to some f(x), and that f(x) is continuous, differentiable, and integrable on [-1,1]. I know how to show that f(x) is continuous, since each fn(x) is continuous, and I fn(x)...

Do you mean going ahead and saying δ<1 (or some number) so that |x-c|<1, implying x>(1-c)? I tried something of that sort but ran into some issues, because the bound still depended on the value of c.

I'm actually trying to see how small it gets. Hence, I need |x2/3 + (cx)1/3 + c2/3| to be greater than some fixed value.

Sorry, I should've showed my earlier steps. I already started working on |x^{\frac{1}{3}} - c^{\frac{1}{3}}|. From there, I multiplied the numerator and denominator to get to [|x-c|/|x2/3 + (cx)1/3 + c2/3|]<ε Now I have my |x-c|, but I can't come up with a lower bound on the denominator...

Thanks for your quick response! Unfortunately, we haven't gotten to the chapter on derivatives yet, and we're only allowed to use an epsilon-delta proof..

Homework Statement Prove x^(1/3) is continuous on all of ℝ. The Attempt at a Solution I've essentially gotten everything to the following point: [|x-c|/|x2/3 + (cx)1/3 + c2/3|]<ε I'm having trouble coming up with a lower bound for the denominator. Any help? Thanks in advance!

Thanks again!

Hahaha, thanks for your help. The only reason I was confirming is that my professor essentially said what you said, and we're supposed to give another type of argument.. I just wanted to make sure that if 3 divides p and 5 divides p, 15 divides p. Lol, making sure I'm not making things up!

Hmm, well one of my main questions is if it's valid to say that 15 divides p and q, with the lcm argument. Does that park make sense?

Homework Statement Prove Square Root of 15 is Irrational The Attempt at a Solution Here's what I have. I believe it's valid, but I want confirmation. As usual, for contradiction, assume 15.5=p/q, where p,q are coprime integers and q is non-zero. Thus, 15q2 = 5*3*q2 = p2...

Thanks for the responses. Sounds like it's just a matter of seeing the bigger picture rather than getting caught up in any particular difficult definition.

Real Analysis will be the most rigorous, proof-based course I've taken for my math major, and I'm concerned because a lot of people at my school HATE the course. Any tips on preparation? Surviving?

Actually, scratch that: I might have figured it out. For those sequences in g(n-1), do you add 1 to the last number in each sequence? That would give you a sequence which sums to n. For those sequences in g(n-2), you append a 2 to the sequence?