Question

Hello! I was wondering if someone can help me with this question? (Will be posted below.)

Answer 1

Find the limit as it approaches infinity when \[\frac{4x-1}{x} < f(x) < \frac{4x^2+3x}{x^2}\] for all x>5.

Answer 2

you need to find out what x is?

Answer 3

or you need the answer?

Answer 4

Im just trying to figure out where to begin. :) Thank you!

Answer 5

@welshfella

Answer 6

He will help you a lot then

Answer 7

Is it 4?

Answer 8

no

Answer 9

sorry cant help with this one

Answer 10

lol

Answer 11

is this a multiple choice question?

Answer 12

Nope!

Answer 13

ok good

Answer 14

10x^2

Answer 15

Alright, thanks!

Answer 16

:D

Answer 17

Take limit of left side,\[\large\rm \lim\limits_{x\to\infty}\frac{4x-1}{x}=a\]It will approach some value.

Take limit of the other side,\[\large\rm \lim\limits_{x\to\infty}\frac{4x^2+3x}{x^2}=a\]You'll find that they approach the same value!

So by Squeeze Theorem: \(\large\rm f(x)\to a\) as \(\large\rm x\to\infty\).

It's a little disturbing that you have strict inequalities.. those shouldn't be strict. Maybe a typo?
Anyway, yes 4 sounds right! :)