not sure to put this in pre calculus or calculus, sorry if mistaken
Find the following limit.
Given that where ,
the answer given is:
i don't understand how and is found.
what i find instead is and
using that, i also find
but please help explain the steps, as the steps in the answers are pretty different from those that i use, im afraid that i've mistaken
"as goes from to , goes from 0 to -1, so the absolute value goes from 0 to 1"
that's how the answer says, but how can we say that 'so the absolute value goes from 0 to 1'? that would be , which is the same as , but what we have found so far is actually only , not as well.
and the question gives , so taking that into account, , and that's how i get for the part of the question.
All of the things you say are true. But when we say that , we're not saying that takes on all possible values that fit the inequality. We're only saying that whatever values of takes on, the inequality holds.
So for every value of , , it is true that , even though, as you said, there are other values of which would also make the statement true.