Recent content by LaMantequilla

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    Delta-Epsilon Proof: Determine Limit l for f(x) = x4

    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...
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    Delta-Epsilon Proof: Determine Limit l for f(x) = x4

    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...
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    Prove that x is irrational unless it is an integer.

    Thank you so much! I can't believe I missed that! Thanks!
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    Prove that x is irrational unless it is an integer.

    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...
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    Undergrad Oblique Asymptotes: What happens to the Remainder?

    That makes perfect sense! Thank you so much!
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    Undergrad Oblique Asymptotes: What happens to the Remainder?

    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...
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    Proving Set Inclusion: P(A) ⊆ P(B) Implies A ⊆ B

    Thanks!
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    Proving Set Inclusion: P(A) ⊆ P(B) Implies A ⊆ B

    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...