GAIN AN ADVANTAGE
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Lesson Specific Problems
- Prove that if \[\lim_{x\to a}\,g(x)=0\] then the limit \[\lim_{x\to a}\,\frac{1}{g(x)}\] does not exist.
- Prove that if \[ \lim_{x\to a}\,f(x)=L\neq 0 \] and \[ \lim_{x\to a}\,g(x)=0 \] then the limit \[ \lim_{x\to a}\,\frac{f(x)}{g(x)} \] does not exist.
- Prove that \[\lim_{x\to a}\,\frac{1}{x-a}\] does not exist.
- Prove that \begin{equation}\lim_{x\to 0}\frac{1}{x}\end{equation} does not exist.
- Determine \begin{equation}\lim_{x\to 5}\,\frac{2x^3-5x^2+6x-15}{x-5}\end{equation}
