Example

Here is another example.

3 3- x- x3 -3 1 lim 3-+-x---x- = lim x2 +-x2---x2-= lim x2-+-x --x = - ∞ x→∞ x2 + 1 x→∞ xx22 + 1x2 x→ ∞ 1+ 1x2

because as x →∞, the first two terms of the numerator are becoming negligible (going to 0), while the last term in the numerator is becoming very large. Thus, the whole numerator is moving toward -∞ while the denominator is going to +1.

See the other full example on the analysis page.

Return to the Limits at Infinity page.