Question

find the limits if they exist and find the indicated value.
Let y(x)=|3x|/x
a) lim y(x)
as x approaches 0+
B) lim y(x)
as x approaches 0-
C)lim y(x)
as x approaches 0
D) y(0)
pleas show step bye step please n explain well..
thanks =)

Answer 1

A)3
B)-3
C)Undefined
D)Undefined

Answer 2

A)Evaluate for x = 1
B)x = -1
C)Since A does not = B, dose not exist
D)Division by zero error.

Answer 3

\[x>0 =>|3x|=3x, x<0=>|3x|=-3x\]

Answer 4

function is
\[f(x) = \frac{|3x|}{x} = \left\{\begin{array}{rcc}
3& \text{if} & x > 0 \\
-3& \text{if} & x < 0
\end{array}
\right.
\]
so as you go to 0 from the left you get -3
from the right you get 3
and since those numbers are not the same the limit does not exist at 0

Answer 5

that is a good looking piecewise function :)

Answer 6

yep

Answer 7

those be the steps, and props to zarkon for letting me still his latex

Answer 8

*steal

Answer 9

i like i didn't know you could do that with latex

Answer 10

i actually found it on the web but zarkon added the nice text box

Answer 11

http://cjohnson.tumblr.com/post/26289015/latex-tip-piecewise-functions

Answer 12

how was work?

Answer 13

i'm sleepy since i had to wake up early
but work was okay (boring meeting)
i come back later and play with it

Answer 14

watching movie :)

Answer 15

good movie i hope. enjoy

Answer 16

First of all remember the definition of absolute value: \[\left| x \right| = x \] for \[x > 0\] and \[\left| x \right| = -x\] for \[x < 0\] therefore you have that \[\left| 3x \right|/x = 3x/x = 3\] for \[x > 0\] and \[\left| 3x \right|/x = -(3x)/x = -3\] for \[x <0\] Therefore the lim as x tends to \[0^{+}\] we just look which x satisfies that and clearly is the one which has \[x >0\] therefore it is 3. Now the lim as x tendo to \[0^{-}\] we just look which x satisfies that and clearly is the one which has \[x < 0\] which is -3. Therefore since both limits are different then the lim as x tend to 0 is not defined.

Answer 17

little slow there jobh8810....but I'll give you a medal anyway ;)

Answer 18

sorry I'm new at this so I'm still learning how to use it hahaha, Peace, Love and Happiness from Puerto Rico

Answer 19

thanks

Answer 20

Peace, Love and Happiness from Pennsylvania :)

Answer 21

nice, I was at Penn State University last August for the MASS program, it was pretty tought but I loved it

Answer 22

nice

Answer 23

from pa? nice

Answer 24

not originally. I moved to PA for my current position.

Answer 25

why r u still looking at this?

Answer 26

myin could you help me out real quick?