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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
Determine \[ \lim_{x\to 2}\frac{x^2+2x-24}{x-2}. \]
Determine \[ \lim_{x\to -3}\frac{x^3+27}{x+3}. \]
Prove that \begin{equation} \lim_{h\to 0}\,\frac{1}{\sqrt{x+h}+\sqrt{x}}=\frac{1}{2\sqrt{x}}. \end{equation}
Determine the limit \begin{equation} \lim_{x\to 3}\,\frac{x^2-9}{x-3}. \end{equation}
Prove that if \[ \lim_{x\to a}\,\left[f(x)+g(x)\right]=M\mbox{ and }\lim_{x\to a}\,f(x)=L \] then \[ \lim_{x\to a}\,g(x) \] exists and is equal to $M-L$.
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