Recent content by jamiemmt

  1. J

    Using limit definition of multivariable derivative

    f(x+h)=x_k+h_k f(x)=x_k so f(x+h)-f(x)=h_k so I am looking for T= the linear transformation, or the value of this limit.
  2. J

    Using limit definition of multivariable derivative

    Hi, everyone- I have a quick question. When you solve for the derivative (as a linear transformation) using the limit definition of derivative, how does it go? For example, let p_k be defined as the projection function from Rn to R, projecting onto kth coordinate of the input value...
    • jamiemmt
    • Thread
    • Definition Derivative Limit Limit definition Multivariable
    • Replies: 2
    • Forum: Calculus
  3. J

    Proving Isometry on Metric: How to Do It

    How do I prove every isometry from R->R is of the form f(x)=a+-x , regardless of the metric? I know it has to do with considering d_1(0,x_1)=d_2(0, f(x_1)), but beyond that I am lost.
  4. J

    Proving R & Null are the Only Clopen Sets of R Without Boundary Points

    So, I know that R and null are clopen, but now to prove they are the only clopen subsets of R... without the idea of boundary points? I know how to do it with boundary points, but can it be done without?
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