Limits

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• Sep 20th 2012, 07:53 AM
Oldspice1212
Limits
Hey guys so I have no idea how to solve limits while looking at a graph, here is the image...

http://i48.tinypic.com/68u4ig.gif
lim
t 0
g(t)

lim
t 0+
g(t)

lim
t 0
g(t)

lim
t 2
g(t)

lim
t 2+
g(t)

lim
t 2
g(t)

g(2)

lim
t 4
g(t)

• Sep 20th 2012, 08:33 AM
Plato
Re: Limits
Quote:

Originally Posted by Oldspice1212
http://i48.tinypic.com/68u4ig.gif
lim
t 0
g(t)

lim
t 0+
g(t)

lim
t 0
g(t)

lim
t 2
g(t)

lim
t 2+
g(t)

lim
t 2
g(t)

g(2)

lim
t 4
g(t)

The answer to the first is $\displaystyle -1$.

The answer to the second is $\displaystyle -2$.

You figure out why. Then do the others and report the answers you get.
We will be glad to help you then.
• Sep 20th 2012, 10:08 AM
Oldspice1212
Re: Limits
So for the third one it would be 2 since from the right it goes towards 2 and from left closest is to the 2?

fourth -2?
fifth 1
sixth 2
7th no idea
8th - 3?
• Sep 20th 2012, 10:21 AM
Soroban
Re: Limits
Hello, Oldspice1212!

Here's part of the solution . . .

Quote:

I have no idea how to solve limits while looking at a graph.
Do you understand "from the left" and "from the right"?
You just trace it with your finger.

Code:

          |         4+                  *           |                *         3+              ♥     *    |            *         2+      o    *           |      *    *       *  1+    * ♥  *           |    *    *     - -*- + - * - o - + - + - -         * |  *1  2  3  4         -1♥ *           |*-         -2o           |
$\displaystyle (1)\;\lim_{t\to0^-}g(t)$
As $\displaystyle t$ approahes 0 from the left, $\displaystyle g(x)$ approaches $\displaystyle \text{-}1.$
Hence: .$\displaystyle \lim_{t\to0^-}g(t) \:=\:\text{-}1$

$\displaystyle (2)\;\lim_{t\to0^+}g(t)$
As $\displaystyle t$ approaches 0 from the right, $\displaystyle g(t)$ approaches $\displaystyle \text{-}2.$
Hence: .$\displaystyle \lim_{t\to0^+}g(t) \:=\:\text{-}2$

$\displaystyle (3)\;\lim_{t\to0}g(t)$
Does not exist.

$\displaystyle (4)\;\lim_{t\to2^-}g(t)$
As $\displaystyle t$ approaches 2 from the left, $\displaystyle g(t)$ approaches $\displaystyle 2.$
Hence: .$\displaystyle \lim_{t\to2^-}g(t) \:=\:2$

$\displaystyle (5)\;\lim_{t\to2^+}g(t)$
As $\displaystyle t$ approaches 2 from the right, $\displaystyle g(t)$ approaches 0.
Hence: .$\displaystyle \lim_{t\to2^+}g(t) \:=\:0$

$\displaystyle (6)\;\lim_{t\to2}g(t)$
Does not exist.

$\displaystyle (7)\;g(2)$
$\displaystyle g(2) \:=\: 1$

• Sep 20th 2012, 10:29 AM
Oldspice1212
Re: Limits
Oh wow thank you so much!! The explanations on approaching helped a ton.
• Sep 20th 2012, 11:37 AM
Oldspice1212
Re: Limits
Quick question for lim g(t)
t - 4

would this = 0 or DNE?