Ahh, yes. It made me laugh when I read it. I would have responded earlier, but I've been terribly busy these past few days.
I'm still having trouble with this proof. Even though I have Spivak's answer, I just don't see how he arrives at it.
Using the (a2)2-(b2)2 factoring, we end up with...
Homework Statement
Determine the limit l for the given a, and prove that it is the limit by showing how to find a ∂ such that |f(x)-l| < ε for all x satisfying o < |x-a| < ∂.
f(x) = x4 , arbitrary a
(Spivak's Calculus 5-3iv)
Homework Equations
The Attempt at a Solution
l = a4
The best I...
Homework Statement
This is taken from an answer book that I have. I don't understand the bolded step. Can someone explain it to me?Suppose x = p/q where p and q are natural numbers with no common factor. Then:
pn/qn + an-1pn-1/qn-1 + ... + ao = 0
and multiplying both sides by...
Let's say I'm trying to find the oblique asymptote of the function:
f(x)=
-3x2 + 2
x-1
Forgive my poor formatting.
So because the denominator isn't linear, we do polynomial long division of the function and ultimately get -3x - 3 as our quotient, with a remainder of...
Homework Statement
Prove that if P(A) \subseteq P(B) then A \subseteq B,
where A and B are two sets and P symbolizes the power set (set of all subsets) of a particular set.
Homework Equations
The Attempt at a Solution
Okay, so here goes.
Because it's a conditional, we suppose...