Take the tour ×  I am asked to find the Limit for:
$$\lim_{x\rightarrow -∞}(x^4+x^5) $$  The first thing I am
tempted to do is divide the numerator and denominator of this
fraction by the highest power of x, in this case $x^5$.
$$\lim_{x\rightarrow -∞}\frac{\dfrac
{x^4+x^5}{x^5}}{\dfrac1{x^5}}$$  Continuing with this I apply
the limit laws which state $\lim_x=0$ when dealing with a limit
at infinity, and I end up with a denominator equal to zero..
share|improve this question add comment  2 Answers  up vote 1
down vote accepted  Just factor it:   As $x\to-\infty$, what’s
happening to $x^4$ and to $1+x$? What’s the combined effect?
share|improve this answer If I was to apply the Limit Laws to
this factored form, how would I end up with a value for a
horizontal Asymptote? –  Kurt Jun 11 '12 at 5:20 @Kurt: It has
no horizontal asymptote. –  Brian M. Scott Jun 11 '12 at 5:29 So
the Limit of this function as x approaches negative infinity, is
going to be negative infinity? –  Kurt Jun 11 '12 at 5:34 @Kurt:
That