Question

Solve the limit

limit(x-->+infinity) sqrt((x-3)/x)

Answer 1

the square root grows slower
so the limit will be zero

Answer 2

Divide both numerator and denominator by x, to solve it algebraically.

Answer 3

I am sorry the actual epression is sort(x-3/x)

Answer 4

sqrt((x-3)/x)

Answer 5

\[\lim_{x\to \infty}\sqrt{\frac{x-3}{x}}\]?

Answer 6

Yes thats correct

Answer 7

then it is one since \(x-3\) and \(x\) grow at the same rate

Answer 8

think what it would be like if \(x\) was \(1,000\) you would have
\[\sqrt{.993}\]

Answer 9

\[\Large \lim_{x\to \infty}\sqrt{\frac{x-3}{x}} = \sqrt {\lim_{x\to \infty}\frac{x-3} {x}}\]

Answer 10

bro I am trying to solve this limit actually http://screencast.com/t/Yoo5IO0bRPjD

And I ended up in the expression above, but what you give me isnt the final answer, something must be wrong :(

Answer 11

@Christos that's a completely different expression... break it up using limit laws.

Answer 12

@satellite73

Answer 13

ohh let me try hold on

Answer 14

What do you mean by limit laws?

Answer 15

\[\Large = \lim_{x \rightarrow \infty} \sqrt{x^2 - 3x} -\lim_{x \rightarrow \infty} x\]

Answer 16

http://www.math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/SandS/lHopital/limit_laws.html

Answer 17

so thats infinity - infinity - infinity = +infinity?

Answer 18

From a graph it looks like it'll be -1.5, I'm just trying to find a way to show that algebraically.

Answer 19

It's ok man dont brother I found it thank you

Answer 20

Yeah i'm glad i didn't try to do it myself... wolfram gives a looooong solution: http://www3.wolframalpha.com/Calculate/MSP/MSP35891gdgbb0f2cc1ecie00005387i303c364idgg?MSPStoreType=image/png&s=42&w=433&h=1816