Recent content by Math_Geek

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    Does g(x) Approach Infinity Given f(x)'s Limit and Inequality Conditions?

    Homework Statement Prove: If the Limit as x goes to a of f(x)=infinity and g(x)>or equal to f(x) for all x in the reals, then limit as x goes to a of g(x) is inf Homework Equations using delta epsilon The Attempt at a Solution for all e>0 there exist a delta>0 s.t g(x)<e now using...
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    Proving the Limit of 1/f(x) When f(x) Goes to Infinity

    yes it is!
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    Proving the Limit of 1/f(x) When f(x) Goes to Infinity

    got it thanks
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    Solved: Analysis Question - Show Exists Interval f(x)>0

    how do I know it is in the interval around a?
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    Proving the Limit of 1/f(x) When f(x) Goes to Infinity

    it is something our teacher showed us how to do, but it never seems to work for me. One more question, we (meaning you) showed the limit is equal to zero becasue 1/M <epsilon? I get confused because we let m>0. so how can the limit be =0.
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    Proving the Limit of 1/f(x) When f(x) Goes to Infinity

    i understand but what is [tex]? at the top, I am not sure what that is. thanks.
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    Proving the Limit of 1/f(x) When f(x) Goes to Infinity

    [b]1. Homework Statement [/bProve Prove: If the limit as x goes to a of f(x)=infinity, then lim as x goes to a of 1/(f(x) =0 Homework Equations Need to show with a delta-epsilon proof The Attempt at a Solution using the definition, lim as x goes to a f(x)=infinity means that for any...
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    Proving Infinite Limit using Delta-Epsilon: One More Limit Homework Statement

    no the problem says it goes to inf
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    Proving Infinite Limit using Delta-Epsilon: One More Limit Homework Statement

    is the definition right?
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    Proving Infinite Limit using Delta-Epsilon: One More Limit Homework Statement

    Homework Statement lim as x goes to 1 from the right of 2^1/x-1=inf Homework Equations solve using delta-epsilon The Attempt at a Solution i am not sure how to prove an infinite limit, I have a defn that states, If for epsilon>0 there exists an M>0 such that x>M implies...
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    Proving the Limit of x^2sin(1/x) as x Approaches 0 Using Delta-Epsilon Proof

    the limit is 0, I think this because it given, also I know sin(1/x) is bounded by so that leaves x^2, so if I choose my epsilon to be sqrt epsilon. then when you square the x then x^2<epsilon Right?
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    Proving the Limit of x^2sin(1/x) as x Approaches 0 Using Delta-Epsilon Proof

    Homework Statement limit as x goes to 0 of x^2 sin(1/x)=0 Homework Equations Use delta-epsilon proof The Attempt at a Solution So |f(x)-L|=|x^2 sin(1/x)|=|x^2||sin(1/x)| and I know that sin(1/x) is bounded by one. I am not sure how to finish because of the x^2.
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    Analysis Question, I posted yesterday

    Both of these lines will intersect at the point (3,6), and you would have to make epsilon= e/2 to satisfy both functions when x is either rational or irrational.
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    Analysis Question, I posted yesterday

    [SOLVED] Analysis Question, I posted yesterday! 1. Homework Statement Define f(x)=2x, x is rational and x+3 when x is irrational. Find all points where g(x) is continuous and prove continuity at these points 2. Homework Equations From analysis homework and using the real definition of...
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    Proving Continuity of Functions on the Reals

    ok so how does the f(x1)+f(x2) play into it?