In this video, I showed how to evaluate a limit of log finctions as x goes to infinity or -infinity. Note that the horizontal asymptote of a function is th elimit at infinity
your videos are so amazing the audio quality is incredible, your voice is so soothing, it's so wholesome seeing you happy solving an equation I've already finished high school, but i pop in sometimes just to watch your math videos
You could also realise that for large x, the 1- (numerator) and the +3x^2 won't significantly impact the function so you get -x/sqrt(4x^2) which is -x/2x which is -1/2
So the definition of absolute value is if x is equal or greater to 0, |x|=x, whilst if it’s smaller than 0, |x|=-x, that of course, because assume that x=-4, which is smaller than 0, of course, u’d have |-4|=-(-4)=4, which is always positive :) and due to the limit approaching negative infinity, we are certain that x would be negative, or smaller than 0, aka |x| would indeed equal -x, it’s just that x is negative, so -x is positive
