Recent content by aesailor

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    Curvature Behavior of a Parametric Curve in R3

    Homework Statement Find a parametric curve in R3 that has zero curvature at the origin and infinite curvature as the parameter t goes to infinity. 2. The attempt at a solution I was thinking it would look like a spiraled cone with the radius getting infinitely bigger, but I didn't know what...
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    Proof including a one to one function

    Homework Statement if f(x) is a one-to-one function, then g(x) = f(x^3) is also a one-to-one function Homework Equations The Attempt at a Solution Assume f(x) is a one to one function. For a particular element of B, there is at most one element of A which is mapped to it...
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    Vector functions traveling along space curves

    Homework Statement two particles travel along the space curves r1(t)=<t, t2, t3> r2=<1+2t, 1+6t, 1+14t> Do the particles collide? Do their paths intersect? [b]2. Homework Equations if vector r(t)=<f(t), g(t), h(t)>, then lim r(t) t-->a = <lim f(t)t-->a, lim g(t)t-->a, lim h(t)t-->a>...
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    Vector Functions: Show Limit as t Goes to a

    I'm really confused by your response tiny tim
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    Vector Functions: Show Limit as t Goes to a

    Homework Statement Show that the lim r(t)=b as t goes to a if and only if for every \epsilon>0 there is a number \delta>0 such that |r(t) - b| < \epsilon whenever 0<|t-a|<\delta Homework Equations if r(t) = <f(t),g(t),h(t)>, then limr(t) as t goes to a = <limf(t) as t goes to a, limg(t) as...
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    Proof for a higher level math class

    Homework Statement ac | bc if and only if a | b (Note that this is really two implications.) 2. The attempt at a solution The only way I can see going about this proof is by using examples. I know that in ac | bc the c will cancel out in both, but I don't know how to properly word...