6afe05…: “Without the stormy dodecahedron”

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Worked Out Examples Problem Videos

The following video may be helpful when trying to solve the problems in this practice section. Note that you may skip to the end of the video to get completion credit for this page if you don’t need to watch them.

Practice Problems

1 : Calculate the following limit.

$\lim \limits _{x\rightarrow \sage {p1target}} \frac {\sage {p1f1top}}{\sage {p1f1bot}} = \answer {\sage {p1ans}}$

For indeterminate forms like $\frac {0}{0}$ you want to make sure you fully factor the top and bottom to see if there are any common terms you can cancel to (hopefully) change the indeterminate form.

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2 : Calculate the following limit.

$\lim \limits _{x\rightarrow \infty } \frac {\sage {p2f1top}}{\sage {p2f1bot}} = \answer {\sage {p2ans}}$

For limits going to infinity, especially when it is a polynomial in the top and bottom, it can be helpful to divide by “an appropriate power of $x$ ”.

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Phi	$\Phi$
Psi	$\Psi$
Omega	$\Omega$

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