Question

Evaluate the limit using L'Hospital's rule

Answer 1

okay so the original equation is \[\lim_{x \rightarrow \inf} \frac{ x^6 }{ x }\] so I took the derivative f'(x)/g'(x) and got \[\frac{ 6x^5 }{ 1 }\]

Answer 2

so wouldn't the limit just be infinity? but it says infinity is not defined in this context so I did something wrong.

Answer 3

as x->inf, x^5->inf

Answer 4

and yes infinity isn't a number
it just means the numbers get really really huge

Answer 5

your derivative is correct:)

Answer 6

Yes:)
you didn't need L'H"S, it is logical to be so, but oh, well you do what the teacher asks:)

Answer 7

lim go to positive infinity its positive infinity

Answer 8

yes, it is positive infinity.

Answer 9

so why do I put in online, because it is not taking infinity

Answer 10

you can use a code for infinity though, `infty`

Answer 11

it said the answer was 1

Answer 12

It is not taking the word infinity?

Answer 13

check the limit, you might have maid a mistake about how you entered the limit here.

Answer 14

The way it is now,
\[\Large \lim_{x \rightarrow \infty} \frac{x^6}{x}=\infty\]

Answer 15

oh wait a minute its \[x ^{\frac{ 6 }{ x }}\]

Answer 16

perhaps

Answer 17

You don't know what your problem says?

Answer 18

here is a screenshot

Answer 19

\[\large \lim_{x \rightarrow \infty} x^{6/x}\]

Answer 20

\[e^{\ln(x^\frac{6}{x})}=e^{\frac{6}{x} \ln(x)}=e^\frac{6 \ln(x)}{x}\]
use this

Answer 21

take the limit of the exponent as x->inf

Answer 22

gotcha!! thanks!

Answer 23

\[e^{\lim_{x \rightarrow \infty} \frac{6 \ln(x)}{x}}\]