2 lim of functions

[Guest]

Find the limits of the both functions:
[tex]lim_{x->\infty } \frac{x^2 + 5}{x^3}[/tex]
[tex]lim_{x->1} \frac{x - 1}{x^2-1}[/tex]

[Guest]

The first limit is [tex]\pm \infty[/tex] because the power of the denominator is bigger 3 > 2

[Guest]

(x^2+5)/x^3 = 1/x+5/x^3 = 0 + 0 = 0 as x->infinity

(x-1)/(x^2-1) = (x-1)/((x-1)(x+1)) = 1/(x+1) = 1/2 as x->1

[Guest]

The first limit is [tex]\pm \infty[/tex] because the power of the denominator is bigger 3 > 2

Is wrong.
The limit is 0 when the power of the denominator is bigger and [tex]\pm \infty[/tex] when it is the opposite(the power of the denominator is smaller).