of x over natural log of x as x approaches one.

And like always pause this video and see if you can

figure it out on your own.

Well we know from out limit properties this is going to

be the same thing as the limit

as x approaches one of x over

over

the limit,

the limit

as x approaches one

of the natural log

of x.

Now this top limit, the one I have in magenta,

this is pretty straight forward,

if we had the graph of y equals x

that would be continuous everywhere

it's defined for all real numbers and it's continuous

at all real numbers.

So it's continuous to limit as x approaches one of x.

It's just gonna be this evaluated x equals one.

So this is just going to be one.

We just put a one in for this x.

For the numerator here we just evaluate to a one.

And then the denominator,

natural log of x is not defined for all x's,

therefore it isn't continuous everywhere.

But it is continuous at x equals one.

And since it is continuous at x equals one,

then the limit here is just gonna be the natural log

evaluated at x equals one.

So this is just going to be the natural log

the natural log of one.

Which of course

is zero.

E to the zero power is one.

So this is all going to be equal to

this is going to be equal to

we just evaluate it

one

over

one

over

zero.

And now we face a bit of a conundrum.

One over zero is not defined.

It is was zero over zero, we wouldn't necessarily be

done yet but it's indeterminate form

as we will learn in the future there are tools we can apply

when we're trying to find limits and we evaluate it

like this and we get zero over zero.

But one over zero.

This is undefined

which tells us that this limit

does not exist.

So does

not

exist.

And

we are done.