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\textbf{Math 126C: Calculus II}
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\textbf{Quiz 3}\quad \textsl{September 12, 2000}

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\emph{Show all your work and all important steps.}
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1. In the process of inversion, the rate of change of sugar is
proportional to the amount of sugar remaining. Suppose after 1
hour there is 1200~g sugar and after 2 hours there is 800~g sugar
remaining. Determine how much sugar there was initially.

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2. Calculate $\lim_{x\to0}\,\frac{x^2}{\ln(\sec(x))}$.

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3.  Let $f(x) = x + \ln(x)$ and $g(x) = x + \sqrt{x}$. Determine whether
$f$ grows faster than, slower than, or at the same rate as $g$, as
$x\to\infty$.

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