Question

lim (x^6 + 1,000x^3 + 2,000,000)/(4x6 + 9,000x^3)
x→+∞

Calculate the limit algebraically.

If the limit does not exist, say why.
A)The limit does exist.
B)The limit from the left is +∞ whereas the limit from the right is −∞. Since the left and right limits disagree, the limit does not exist.
C)The limit from the left is −∞ whereas the limit from the right is +∞. Since the left and right limits disagree, the limit does not exist.
D)It is not possible to evaluate a function at x = ∞; therefore the limit does not exist.

Answer 1

Have you learned end behavior? Or do you remember it?

Answer 2

i know when x→+∞ its +∞ but it says its wrong

Answer 3

and chose D as an answering

Answer 4

Try dividing by x^6:
\[\LARGE \frac{(x^6 + 1,000x^3 + 2,000,000)}{(4x6 + 9,000x^3)}\]

Answer 5

It's hard to do it with latex..
but when you do, you'll get something like:
(1+{1000/x^3}+{2000000/x^6})/4+{9000/x^3})

Answer 6

Once you do that, plug in infinity:
Leaving:
\[\LARGE \frac{1}{4}\]
any number over infinity is 0.

Answer 7

Since infinity is limitless, it will continue to grow, while the numerator stays the same.. eventually the denominator will be so great that it will practically be 0.

Answer 8

Also, with end behavior, learned in Algebra II, you could take the highest powers:
\[\LARGE \frac{(x^6 + 1,000x^3 + 2,000,000)}{(4x6 + 9,000x^3)}=\frac{x^6}{4x^6} \]
Get rid of the x's
\[\LARGE \frac{1}{4}\]

Answer 9

Okay, I gtg now, hope I made it understandable, good luck!

Answer 10

thank you