Question

Fine the limit as x approaches negative infinity of x cubed minus four x squared plus five.

Answer 1

Well, we can just kind of think of the graph itself and can get a quick answer. First off, this isn't a rational function or anything that will give us a fraction, so no worries about asymptotes or anything. Secondly, we can use the leading coefficient test. We have a degree 3 polynomial that is positive, meaning we come from negative infinity on the bottom left and go to infinity to the top right. So if you're approaching negative infinity, you're just going back downwards to negative infinity in the bottom left of your graph. So its just negative infinity.

Answer 2

If you don't know how to do a limit, try it on your calculator and see what you get, so try putting in "bigger and bigger" negative values into \(x^3-4x^2+5\) and see what it tends to. As @Psymon remarked, it will not tend to anything, but just get larger in absolute value but stay negative.

Answer 3

If you wanted to know what \[\lim_{x\rightarrow0^+}x^x\]
is, just put in \(x=0.001\) and then \(x=0.0001\) etc. It's always easier to show something when you already know what the answer is.

Answer 4

\[\lim_{x\to -\infty}~x^3-4x^2+5\] now you need to put the \[-\infty\] at the highest x, in this case wil be \[x^3\] then we can write \[\boxed{\boxed{\lim_{x\to -\infty}~(-\infty)^3=-\infty}}\]