Question

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

true or false

Answer 1

Pick a really big number

Answer 2

plug it in for x.

Answer 3

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

Answer 4

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?

Answer 5

no?

Answer 6

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

Answer 7

ya

Answer 8

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

Answer 9

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