00:01
Right, so in this problem, we are giving three limit problems.
00:03
Starting with part a, we are giving the limit as z tends to infinity of the expression 4 z squared divided by z minus 1 squared.
00:19
I'm going to write this out as the limit as z tends to infinity of 4 z squared, and on the denominator i'm going to be into z squared minus 2 z.
00:33
And then plus one next here we are basically going to take a look at our the leading terms on the numerator and denominator and this will be equal to the limit as z approaches infinity of the ratios of that that is four z squared over z squared the z squares will cancel out leaving us with four over one so the limit here is just simply going to equal to four so this is the quick way to do this next for part b, we have the limit as z tends to 1 of 1 over z minus 1 squared.
01:16
And for that, i would like to write down a number line.
01:21
And in this number line, we place the zeros of the top and the zeros of the denominator.
01:25
We only have a 0 is equal to 1 on the denominator.
01:29
This is representing a vertical asymptote because it's a zero of the denominator...