So you could have a situation like this, where you have a gap right over there and looks something

limit as x approaches zero from the right of f of x.

So it's approximately linear around F of X equals zero, but it levels off to zero and one as we go to the extremes.

Sorry for taking it out of the final exam.

So the limit of f of x should be equal to f of zero which should be equal to the limit as we approach from the right.

When you look at those numbers, most of them are actually pretty good guesses.

And that puts you out in the extremes of the T distribution or that Z distribution.

Geographic Pole

I think it's atrocious.

In this case, the limit as you approach the expression is equal to evaluating the expression of that value.

It's a bit like this imagine that we'd only ever encountered Euclidean space.

Polar

This right here is the point (1.5, 1) and if we approach it from the left hand side, from values less than it it's one, the limit seems to be one and if we approach from the right hand side the limit seems to be one

You two really underdo it.

We believe there's some water in the polar caps, there are polar caps of North Pole and South Pole.

So the two limits from the left and the right both exist and the limit at that point would exist, but if the function itself doesnt equal that value there, if it equals something else, then the function would not be continuous.

If we just put here change in x is 0 you are going to get something undefined.

I literally use it all the time.

Antarctica

circumpolar

Magnetic Pole

Polar Chart

Top Secret

Antarctica.

Cathode.

Anode.

That's called a value.

The probability of landing way out there given the assumption that the null is true is really low.

And so that's what we've done with this ship.

Polar Coordinates

Circumpolar

Arctic Circle

The Great North.

Antarctic

I'd like you to tell me for any two variables x and y, if they're not perfectly related that is if the absolute value of their correlation is not 1 how extreme is our y prediction compared to x?

The South Pole is a lot colder than the North Pole.

The devices that computers use are what's called a transistor.

So maybe we sell a shoe and it becomes the greatest shoe you ever wore ... the greatest car you ever drove from The Greatest Movie Ever Sold, the greatest drink you've ever had, courtesy of The Greatest Movie Ever Sold.

Maybe one more thing might help. Have you ever played with two magnets?

It's no more than an anode and a cathode separated by an electrolyte, right?

And these are the exact formulas I used in the exact case.

And the answer is zero, nothing else but zero.

Physically, the way you can think of it is, the Jeans Length is the size of the collapsing cloud, where the sound waves can cross before it collapses.

Polar Line of a Point

Polar Equation