Limits...!! lim (2-x) / (x²-2x-8) as x -> 4+, etc

I

ihatecalc

New member
Joined
Sep 11, 2006
Messages
22
Limits...!! lim (2-x) / (x²-2x-8) as x -> 4+, etc

I have a test on limits tomorrow and my mind has officially gone BLANK! Note: We cannot use calculators.

Please help me with these couple sample questions. Hopefully, I'll be able to understand it then...

. .lim. . . . .(2-x) / (x²-2x-8)
x--> 4+


. . .lim. . . . . .|x+4| / (2x-9)
x--> infinity


. .lim. . . .(sin²x)/(3x²)
x--> 0
 
Use L'Hopital (take the derivative of the top, and of the bottom. I'll do the first as an example)


lim (2-x) / (x²-2x-8)
x--> 4+

= lim -x / (2x-2)
x--> 4+

=-4/6
=-2/3
 
okay, i understand the first one now.

however, i dont know how to take the derivative of an absolute value? or a trig function? can anyone explain please?
 
You can do the same thing I did to example 1 and apply L'Hopital again.

For the second example, since you're going to infinity, here's a nifty trick:

lim |x+4|
-----------------
x--> oo (2x-9)



= lim |x+4| (1/x)
-----------------
x--> oo (2x-9) (1/x)



= lim 1 + 4/x
-----------------
x--> oo 2 - 9/x


see where I'm going with this? You divide both the numerator and the denominator by the highest power x. Now you do the rest.
 
well you cant get -OO on that because it has a function of x over a function of x (meaning x in both numerator and denominator) ex: x/(x+4)

For it to be oo it has to be a constant over a function of x (meaning x only in denominator) ex: 3/(x+4)
 
You must log in or register to reply here.
Top