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  1. Vahsek

    Limits lim x→3+ = 81-x4/(x2-6x+9)2

    Indeed, substituting 3 means that you would have 0 in the denominator, so the original expression would diverge as x → 3+. Therefore, you could argue that there is no limit since the expression would not converge to any real number per say. That being said, I feel that a more precise answer...
  2. Vahsek

    Limits lim x→3+ = 81-x4/(x2-6x+9)2

    You've already done the first step: that is to cancel out common factors in the numerator and denominator so that you don't get 0/0.
  3. Vahsek

    Basis for a Nul Space

    The way to find a basis for the nullspace is to identify all the free variables (which correspond to the free columns of the matrix): x1 and x3 are the free variables while x2 is a pivot variable. Since the number of free columns (or number of free variables) equals 2, you will get 2 special...
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