Please determine the following limit if they exist. If the limit doe not exist put DNE.
lim 2x^3 / x^2 + 10x - 12
x->infinity.
Thanks.
Intuitively I can see that the numerator gets larger at a faster rate than the denominator.
e.g. if x = 1000, the top is 2 billion, but the bottom is only approx. 1 million, so the expression has a value of about 2000
So the limit approaches infinity.
Algebraically, divide each term by x^2 to get
limit (2x/(1 + 10/x - 12/x^2)
so as x --- infinity
both 10/x and 12/x^2 ---> 0
so we have 2(huge)/1 which appr. infinity