Question

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.

Answer 1

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