y is equal to g of x.

グラフがあります。

What I wanna do is I wanna figure out

6より小さい数字から

the limit of g of x

xの値が6に近づきときの

as x approaches positive six

g(x)の極限を

from values that are less than positive six

求めてみよう

or you could say from the left, from the, you could say

左側からといってもいいし

the negative direction.

マイナスの方向からといってもいいね

So what is this going to be equal to?

極限は何になるかな？

And if you have a sense of it, pause the video

もし心当たりがあるようだったら動画を止めて

and give a go at it.

自分でやってみて

Well, to think about this,

これを解くには

let's just take different x-values that approach six

左から6に近づくいくつかのxの値を取ってみて

from the left and look at what the values

関数の値がどうなるかを見てみるのがいい

of the function are.

g(2)は1より少し大きい

So g of two, looks like it's a little bit more than one.

g(3)はそれより少し大きい

G of three, it's a little bit more than that.

g(4)は2より少し下

G of four, looks like it's a little under two.

g(5)は3くらい

G of five, it looks like it's around three.

g(5.5)は5くらい

G of 5.5, looks like it's around five.

g(5.75)は

G of, let's say 5.75,

9くらいかな

looks like it's like nine.

だからxが左側から6に近づけば近づくほど

And so, as x gets closer and closer to six

関数の値は...

from the left, it looks like the value of our function

無限に大きくなっている

becomes unbounded, it's just getting infinitely large.

ここで極限が無限に等しいと

And so in some context, you might see someone

こんな風に書く人がいるかもしれない

write that, maybe this is equal to infinity.

でも無限って言うのは

But infinity isn't, we're not talking

特定の数字をとっているわけじゃないんだ

about a specific number.

極限というのを

If we're talking technically about limits

厳密にいうと

the way that we've looked at it, what is,

この書き方をもしかしたら 授業で見るかもしれないけど

you'll sometimes see this in some classes.

でもこのKhan Academyの練習では

But in this context, especially on the exercises

この極限は存在しないというよ

on Khan Academy, we'll say that this does not exist.

存在しない

Not exist.

これは無限になっている

This thing right over here is unbounded.

面白い、左側の極限は存在しないのに

Now this is interesting because the left-handed limit here

右側の極限は存在する

doesn't exist, but the right-handed limit does.

xの値が右側から6に近づくときの

If I were to say the limit of g of x

g(x)の極限は

as x approaches six from the right-hand side,

考えてみよう

well, let's see.

g(8)はここ、g(7)はここ

We have g of eight is there, go of seven is there,

g(6.5)、見た感じ

g of 6.5, looks like it's

-3より少し小さい

a little less than negative three.

g(6.01)、-3にもっと近い

G of 6.01, little even closer to negative three.

g(6.0000001)は-3にとても近い

G of 6.0000001 is very close to negative three.

だからこの極限は

So it looks like this limit right over here,

少なくともグラフ上

at least looking at it graphically,

右側から6に近づくとき

it looks like when we approach six

この関数は

from the right, looks like the function

-3に近づいているように見える

is approaching negative three.

でも左からだと無限になっている

But from the left, it's just unbounded,

だから極限は存在しない

so we'll say it doesn't exist.