For the polynomial
ƒ(x)=1-2x+5x^4
as
x--∞,ƒ(x)---∞

true or false

Question

For the polynomial
ƒ(x)=1-2x+5x^4
as
x-->∞,ƒ(x)-->-∞

true or false

anonymous · Answer

Pick a really big number

anonymous · Answer

plug it in for x.

anonymous · Answer

Or you can just think about what would happen if x gets really big and positive.

anonymous · Answer

1 isn't gonna change as x changes.

-2x will get big and negative as x gets big and positive

+5x^4 will get big and positive as x gets big and positive.

So will -2x get more negative than 5x^4 gets positive?

anonymous · Answer

no?

anonymous · Answer

Does the graph y=5x^4 go up faster than y=2x

anonymous · Answer

ya

anonymous · Answer

Right, so 5x^4 is going to go up faster than -2x is going to go down. Therefore the result will be +$\infty$ not $-\infty$

anonymous · Answer

I asuume this is a calc question...$$\lim_{x \rightarrow \infty} (1-2x+5x ^{4}) = \lim_{x \rightarrow \infty} f'(x)= \lim_{x \rightarrow \infty} (-2+20x ^{3}) =+\infty$$