lim x-infinity of f(x) = x^2 - x^4

Question

lim x->infinity of f(x) = x^2 - x^4

misty1212 · Answer

HI!!

anonymous · Answer

any way to show mathmatically the intuitive negative infinity?

misty1212 · Answer

guess, i bet you will be right
if it is not obvious, try $x=100$ and see what you get

anonymous · Answer

right, so infinity minus infinity squared is negative infinity

misty1212 · Answer

there is no such thing as infinity minus infinity squared

anonymous · Answer

so, how would you write that?

misty1212 · Answer

not sure what you mean 
writing things like $\infty-\infty$ is just a from, a shorthand for limits

anonymous · Answer

i guess I'm asking you to prove what is obvious via algebra

misty1212 · Answer

oh i see

misty1212 · Answer

yo would show (maybe with some algebra that given any $N>0$ there is an $x$ such that 
$$x^2-x^4<-N$$

anonymous · Answer

sounds like profs may just accept intuition in this case...

michele_laino · Answer

Please note that I can rewrite your function as below:
$$x ^{2}-x ^{4}=x ^{4}\left( \frac{ 1 }{ x ^{2} }-1 \right)$$

anonymous · Answer

so, always a good idea to factor out highest degree of x?

michele_laino · Answer

yes! I think it is the standard procedure

anonymous · Answer

how do you get from there to negative infinity?

anonymous · Answer

oh, duh, I see it now, (0-1) * infinity

michele_laino · Answer

please note that 
x^4 is not an undetermined form, and
also (1/x^2  -) is not an undetermined form, so their limit exist and you can apply the rule of multiplication of limits

michele_laino · Answer

opps...also (1/x^2  -1) is not an undetermined form

anonymous · Answer

thanks all for helping

michele_laino · Answer

thanks!