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\frametitle{Calculating Limits using Limit Laws}

We have seen that calculating limits with a calculator sometimes leads to incorrect results.
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We will now see how to compute limits using \emph{Limit Laws}:
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\begin{block}{}
Let $c$ be a constant, and let $\lim_{x\to a} f(x)$ and $\lim_{x\to a} g(x)$ exist.
Then
\begin{enumerate}
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\item $\lim_{x\to a} \;[f(x) + g(x)] = \lim_{x\to a} f(x) + \lim_{x\to a} g(x)$
%         \\ \textcolor{gray}{(The limit of the sum is the sum of the limits)}
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\item $\lim_{x\to a} \;[f(x) - g(x)] = \lim_{x\to a} f(x) - \lim_{x\to a} g(x)$
%         \\ \textcolor{gray}{(The limit of the difference is the difference of the limits)}
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\item $\lim_{x\to a} \;[c \cdot f(x)] = c \cdot \lim_{x\to a} f(x)$
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\item $\lim_{x\to a} \;[f(x) \cdot g(x)] = \lim_{x\to a} f(x) \cdot \lim_{x\to a} g(x)$
%         \\  \textcolor{gray}{(The limit of a product is the product of the limits)}
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\item $\lim_{x\to a} \frac{f(x)}{g(x)} = \frac{\lim_{x\to a} f(x)}{\lim_{x\to a} g(x)}$ if $\lim_{x\to a} g(x) \ne 0$
\end{enumerate}
\end{block}
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These laws also work for one-sided limits $\lim_{x\to a^\pm}$.
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