Question

Find the derivative of the limit as x approaches infinity

Answer 1

\[\frac{ \sqrt{x^4+5x^3-1} }{ 2x^2+7 }\]

Answer 2

\[\rm\lim_{x \rightarrow \infty} \frac{ \sqrt{x^4+5x^3-1} }{ 2x^2+7 }\] For these types, you want to analyze what your biggest power is. In this case it's \(\rm x^4\)

Answer 3

\[\rm \sqrt{x^4} = x^2\] So you're going to divide all your terms by \(x^2\). Inside the parenthesis, you will divide by \(x^4\)

Answer 4

so \[\frac{ 2x }{ 2 + 7}\]

Answer 5

\[\rm\lim_{x \rightarrow \infty} ~ \dfrac{d}{dx} \frac{ \sqrt{x^4+5x^3-1} }{ 2x^2+7 }\]

like this ?

Answer 6

\[\rm \lim_{x \rightarrow \infty} \frac{ \sqrt{x^4/x^4 +5x^3/x^4 -1/x^4} }{2x^2/x^2 +7/x^2}\]

Answer 7

if the limit exists, then the derivative of it is 0...

Answer 8

\[\frac{d}{dx}(\lim_{x \rightarrow a}f(x)) =0 \text{ if the limit exists }\]

Answer 9

if the limit doesnt exist also derivative of a limit would be 0 i think.. but the question becaomes interesting if it is limit of a derivative

Answer 10

if the limit doesn't exist
then I would think the derivative of it would also not exist

Answer 11

\[\dfrac{d}{dx} (DNE) = 0\]

;p

Answer 12

so the limit does not exist then ?

Answer 13

just messing lol, it makes no sense

Answer 14

When you reduce that you shall get \[\rm \lim_{x \rightarrow \infty} \frac{ \sqrt{1+5/x -1/x^4}}{2 + 7/x^2}\] wherever there is an x, you can access that the fraction approaches 0, and you can eliminate it.

Answer 15

@johnnydicamillo I think the wording of your problem is incorrect

Answer 16

okay let me re write

Answer 17

So therefore the limit becomes 1/2.

Answer 18

Thanks @Jhannybean !

Answer 19

just so you know nothing she did involved finding the derivative

Answer 20

i think you just meant to evaluate the following limit:
\[\lim_{x \rightarrow \infty}\frac{\sqrt{x^4+5x^3-1}}{2x^2+7}\]

Answer 21

Ah, @freckles is right.

Answer 22

DO you know why the derivative of a limit is 0? Because when you are approaching a limit, you are approaching one substantial number. I guess you can take it for what it's worth in beginning calculus, it gets more complex later on. So when you take the derivative of a constant, as you may have learned, it will be =0. \(\rm \frac{d}{dx}(c) =0\)