Name: Limits by direct substitution | Limits and continuity | AP Calculus AB | Khan Academy
Uploaded: 2022-07-02T02:57:50.000Z
Duration: 2 min 7 s
Description: 直接替代的極限 |極限和連續性 | AP微積分AB |可汗學院Learn the English Usage: continuous,expression,negative,quadratic,limit,equal,squared,define,proof,graph,defined,jump,substitution,evaluating,upward,visually,continuity,evaluate,standard,calculus,direct,khan...

Modal verbs - A2

- [Voiceover] So let's see if we can find the limit

as X approaches negative one of six X squared

Now the first thing that might jump out at you

is this right over here, this expression could be used

And when you think about this, I'm not doing

a rigorous proof here, parabola would look

upward opening parabola, look something like this.

It is a, this graph, visually, is continuous,

is going to be defined for all values of X

for all real numbers, and it's going to be continuous,

And so if something is continuous for all real numbers,

well then the limit as X approaches some real number

is going to be the same thing, it's just a value

within the expression at that real number.

So what am I saying, I'm just gonna say it another way,

we know that some function is continuous,

is continuous at some X value, at X equals A

if and only if, I'll write that as iff, or iff,

but just, it's conceptually not a big jump

to say, okay, well this is, this is just a standard

and in fact it's continuous for all real numbers.

so that means that the limit as X approaches A

for this expression is just the same thing

So all I have to to is evaluate this at negative one.

This is going to be six times negative one squared

So that's just one, this is negative five,

Subtitles ListPlay Video

Limits by direct substitution | Limits and continuity | AP Calculus AB | Khan Academy

expression

negative

general

function