Question

How do I find the limit of this?

Answer 1

\[\lim_{x \rightarrow \infty} (2x+1)^4 / (3x^2+1)^2\]

Answer 2

Are you familiar with l'hoptal's rule ?

Answer 3

Kind of, is that where you can divide the top and bottom or something?

Answer 4

what do you notice about the top poly and the bottom poly?
as in their degree?

Answer 5

What would be the first term of each polynomial in standard form

Answer 6

you don't really need to multiply these out fully

Answer 7

we just need the first term of each when in standard form

Answer 8

The numerator has a higher degree than the denominator. Would they both be to the 4th degree?

Answer 9

they both have the same degree

Answer 10

the first term on top (when in standard form) is (2x)^4
the first term on bottom (when in standard form) is (3x^2)^2

Answer 11

you only need to consider evaluating the following:
\[\lim_{x \rightarrow \infty}\frac{(2x)^4}{(3x^2)^2}\]

Answer 12

What method could I use to determine this limit? Would it be useful to look at a graph?

Answer 13

have you tried evaluting the limit I gave you?

Answer 14

Yes but I don't know how to approach it.

Answer 15

(2x)^4=?

Answer 16

\[(2x)^4=2^4x^4=? \\ (3x^2)^2=3^2(x^2)^2=?\]

Answer 17

16x^4 and then the other term would be 9x^4

Answer 18

what is x^4/x^4?

Answer 19

1, so would it be 16/9?

Answer 20

\[\lim_{x \rightarrow \infty}\frac{(2x)^4}{(3x^2)^2}=\lim_{x \rightarrow \infty}\frac{16x^4}{9x^4}=\frac{16}{9}\]

Answer 21

yep

Answer 22

That makes so much more sense!! Thank you!!