# But f(-4) is not defined!

Grading my own designed homework assignments is going to be fun (cough, cough, hack). They are intended to be much harder than the online homework and maybe even the exams, so they might take the longest to grade because of all the comments. Here is a smattering of comments from the first homework, on using the laws of limits, including some evaluable indeterminate forms.

• ✓ Why? (-1)
• “0/0” means that you have to do algebra.
• Algebra error.
• $\lim_{x\to 1} h(x)$ doesn’t care about $h(1)$.
• But $f(-4)$ is not defined!
• -3 was a typo.
• ✓ Why? (-1)
• You will be penalized for leaving the cover page blank next time.
• [-.41667] is not an exact answer.
• What about at $x=-4$?
• Please leave roots as is.
• “X” Why? (-4)
• Each of these limits can (and should) be evaluated without a calculator.
• You can further simplify $\cos(\pi/4)$.
• $\lim_{x\to 3} h(x)$ doesn’t care about $h(3)$.
• This trivialized the problem.
• But $f(-4)$ is not defined!
• Is, say, $x=-9$ in the domain?
• Why?
• Wrong answer, but conceptually correct.
• The numerator is zero too.
• Not at $x=-4$.
• Why?