Limits

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September 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)
September 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 $-1$ .

The answer to the second is $-2$ .

You figure out why. Then do the others and report the answers you get.
We will be glad to help you then.
September 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?
September 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 |

$(1)\;\lim_{t\to0^-}g(t)$
As $t$ approahes 0 from the left, $g(x)$ approaches $\text{-}1.$
Hence: . $\lim_{t\to0^-}g(t) \:=\:\text{-}1$

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

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

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

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

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

$(7)\;g(2)$
$g(2) \:=\: 1$
September 20th 2012, 10:29 AM
Oldspice1212

Re: Limits

Oh wow thank you so much!! The explanations on approaching helped a ton.
September 20th 2012, 11:37 AM
Oldspice1212

Re: Limits

Quick question for lim g(t)
t - 4

would this = 0 or DNE?