the 3 could be replaced by any positive (!) number

actually the wording of the question should reflect the limit of the function and not the limit of x

This post was edited by brmv on Sep 17 2013 06:00pm

final problems im stuck on (btw thanks a ton)

4 find the horizontal asymptotes g(x) = (3x+2)/ ( radical(x^2-4))

and

5

f(x)= (2x-9)/(x( radicalx)) supposed to complete a table of values for x/f(x) where the x is 1, 10^1, 10^2, 10^3, and so on. do i simply plug those numbers in for x in the calculator?

please give the definition of 'radical' you are using to avoid confusion [note: studied math in a non-english speaking country]

sorry cant find a key for it on my keyboard


also known as square root? long division sign with the v at the end

kinda like v----

so clarify, for #4 x^2-4 is all under the radical sign
and in #5 only the second x is under the radical

This post was edited by known954 on Sep 17 2013 06:08pm

everything brmv said is right on, but I'd describe it the following way, which has a lot of hand waving, and not rigorous at all, but might help you get a feel for it:

you were working with a fraction, so really its a division problem.... 3 divided by a "really big number"

if you had 3 ounces of soda, and you wanted to divide it evenly among your 1 million friends, how much soda does each friend get? Basically almost none.... And a million isn't even close to infinity. So a constant divided by infinity is essentially equal to 0.

This post was edited by Azrad on Sep 17 2013 06:14pm

i understand the concept better
see,
if you were my calculus teacher, rather then some ex air force drill sergeant bastard, maybe i'd actually learn in class

was thinking you mean square root but was not sure - to avoid confusion i use sqrt(x)

in question 4 there are two points to consider, namely x=-2 and x=+2 but there is one question: do you deal with complex numbers in your course?

in question 5 i assume you are asked for a table of (x,f(x)) and not x divided by f(x), if this is right i would understand the question to just ask you to work those out with a calculator (or by hand)

/postscript

careful careful
methinks 'Azrad' was in the military as well

This post was edited by brmv on Sep 17 2013 06:20pm

i have the utmost respect for soilders


just not this one



e: i plugged it into a math tool i use (wolframalpha.com) and it told me the horizontals were +3 and -3.


i think you are confusing the verticals ( which are +2 and -2) with the horizontals (which are +3 and -3 but i dont know how find that, other then cheating with a graphing calculator)


&yes for 5 its a table of the 2 values, not of division

This post was edited by known954 on Sep 17 2013 06:28pm

and to your question of complex numbers im not entirely sure what you mean (if you mean would my teacher perfer sqrt(3) to some decimal value as an aswer, he would prefer we leave it as a sqrt)

if you are looking for the limits when x goes to +inf and -inf then it is just like question 3, see at 'Azrad's explanation above (assuming you take the positive square root)
sqrt(x^2-4) ~ absolute value of x, ie you get (3x+2)/x now you can forget the 2 for very large x and you have 3x/abs(x)

and if you do not know what a complex number is, forget atm all about it

This post was edited by brmv on Sep 17 2013 06:46pm