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the first one has degree 4, which is even
also it has a positive leading coefficient (it is 1)
therefore as \(x\to \infty\) you have \(x^4+5\to\infty\) and as \(x\to -\infty\) you have \(y^4+5\to \infty\)
do you know what a polynomial of odd degree with negative leading coefficient looks like?
ok lets start with a polynomial of degree 1, a line, with negative leading coefficient, like say \(y=-x+1\) you know what that looks like?
it has the same "end behavior' as any polynomial of odd degree with negative leading coefficient
you got that? goes to positive infinity as x goes to negative infinity, and negative infinity as x goes to positive infinity
So the answer is x^4+5 > infinity
do you know what "end behavior" means?
both a and b are functions that have an odd number as their highest exponential degree. so the as x gets bigger, so does y. and as x gets smaller, so does y. the answer for the limit for both is |dw:1434210988972:dw| |dw:1434211163340:dw|
just keep ∞ and ∞ in the same equation and -∞ and -∞ in the same equation. for both and you're all set