Investigate whether the following limits exist. For those that do exist, state the limit.

Question

anonymous · Answer

attachment

amistre64 · Answer

what does each piece equal to when x=1 ?

anonymous · Answer

Actually, I know where the limits exist or not now but I do not know how to find at which value it exists at.

anonymous · Answer

Can you help me out with these example? I know it has a limit but I do not know how to find it...

amistre64 · Answer

a simple means is to draw the lines ona graph; and find where x=2 is at.

amistre64 · Answer

x-4,x   thats odd

amistre64 · Answer

oh, x-4 , given that x is in the interval

amistre64 · Answer

you do realize that x-4  is the same as x-4 ??

anonymous · Answer

yes I do, but the answers says that there is a limit.

anonymous · Answer

and so there isn't other way of determining the limit for these hybrid functions besides graphing it?

amistre64 · Answer

this isnt a hybrid function :/

amistre64 · Answer

from 0 to inf it is x-4

and everywhere else it is,  x-4

anonymous · Answer

oh k, my bad. so it has to have a quadratic and linear or ....?

amistre64 · Answer

a limit is defined when it approaches the same value from the left or the right (and in higher dimensions youll have to check all directions)

amistre64 · Answer

in this case x=2 falls clearly within the top function (regardless of what the bottom function would be).

amistre64 · Answer

since x-4 has no domain issues at x=2, the limit would be the value at x=2

anonymous · Answer

answer says -2

amistre64 · Answer

2-4 = -2  ues

anonymous · Answer

ok, so it is basically substituting the value of x is approaching into the equation?

amistre64 · Answer

yes

anonymous · Answer

so will it work for this?

phi · Answer

This video might help http://www.khanacademy.org/math/precalculus/v/introduction-to-limits

amistre64 · Answer

notice that -2 is an issue within both intervals, top and bottom

amistre64 · Answer

the only way a limit exists is if it approaches the same value from the left and the right

plug in x=-2 into top and bottom and see if they produce the same value in this case

anonymous · Answer

yes, 0.

amistre64 · Answer

then the limit exists, and is 0

anonymous · Answer

ok, I think I get it now, thanks.

anonymous · Answer

sorry @phi, I tend to stay away from KhanAcademy videos because they are quite messy, confusing and long.

anonymous · Answer

but thanks.