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1969 AMC 12 Question 35

AMC12 · 1969 AMC 12

Question 35

Let $L(m)$ be the $x$-coordinate of the left endpoint of the intersection of the graphs of $y=x^2-6$ and $y=m,$ where $-6\lt m\lt6.$ Let $r=\frac{[L(-m)-L(m)]}{m}.$ Then, as $m$ is made arbitrarily close to zero, the value of $r$ is:
  1. arbitrarily close to zero
  2. arbitrarily close to $\dfrac1{\sqrt6}$
  3. arbitrarily close to $\dfrac2{\sqrt6}$
  4. arbitrarily large
  5. undetermined