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Function Limits V: Properties of Function Limits
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Lesson Summary:
We list here important properties of function limits.
Lesson Inputs:
Function Limits III: The Gory Details
Lesson Outputs:
Properties of Continuous Functions
GAIN AN ADVANTAGE
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Lesson Specific Problems
Prove that \begin{equation}\lim_{x\to a}\,f(x)\,g(x)=LK.\end{equation}
Prove that \begin{equation}\lim_{x\to a}\,\sum_{i=1}^N\,f_i(x)=\sum_{i=1}^N\,L_i.\end{equation}
Prove that \begin{equation}\lim_{x\to a}\,K\,f(x)=KL\end{equation} where $K$ is a constant and \begin{equation}\lim_{x\to a}\,f(x)=L.\end{equation}
Prove that \[\lim_{x\to a}\,[f(x)+g(x)]=L+K.\]
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