Note that as x gets larger, reciprocals of positive powers of x get smaller and smaller, getting closer and closer to zero. In fact, we can get them as close to zero as we like, by making x large enough:

x =	10	1,000	1,000,000
=	0.1	0.001	0.000001
=	0.01	0.000001	0.000000000001

or, as x →-∞

x =	-10	-1,000	-1,000,000
=	-0.1	-0.001	-0.000001
=	0.01	0.000001	0.000000000001

The third line is the result of our analysis of the components of line 2.

because, as x →∞, → 0, 2 → 2, → 0, 1 → 1, and → 0.

See another example worked out.

Return to the computation page.

Return to the Limits at Infinity page.