/sci/ - Science & Math

So if a function is continuous through a, then lim x-->a f(x) = f(a). How miniscule can the continuity be? If you have x defined from 0.999999999 through 1.0000000001, you could use direct substitution and say they are asking for x--->1, is there a rule about how small the continuity can be?

>>10926463
>next time remember to set an alarm at a completely random time differing from the one u are certain the test occurs at after checking multiple times, it will magically turn out to be correct!

When you use a calculator to compute a value for an inverse trig function like cos^-1 that is outside of the domain, what are the values that the TI type calculators are giving you? If you put arccos(2) it will return (0, 1.3169.....). What is this value supposed to be? Why doesn't it just say "error domain" like it sometimes does with other things?

T(0) = 7.5sin(pi/12(0-10))+10.5

How do I solve this? The answer is 6.75 but I can't figure out how

How do I rewrite a^1/2(2a^2 - 4/a)?

My problem says the - 4/a becomes-4a^-1, but how does this happen? They don't explain it