2 2 4. 2 again is equal to 8. is equal to 8

The square of the magnitude of our total displacement is going to be equal to the sum of these two squares

IT WlLL BE EQUAL TO FlNAL VELOClTY SQUARED

YOU WlLL GET, AND I FLlP THEM AROUND, FlNAL VELOClTY IS EQUAL TO

If x is equal to Let's say that x is equal to 1, and y is equal to 8, then this expression would evaluate to (Well every time we see an x, we want to put a 1 there.)

Then once its moving then we can say that this is going to be this will then be equal to this over here will be equal to the force of friction

So our initial velocity is going to be this

If we said x is equal to 2, and y is equal to 3, then this expression would evaluate to, (Let me do in that color.)

Is going to be equal to 1 because now x is 1.

And then I'll just say for i is less than or equal to n, greater than or equal to 1.

My initial velocity is 0, I'll denote it as a vector right here.

And our function is going to be equal to 1, it's getting closer and closer to 1, it's actually at 1 the entire time.

So b is 55. And c is going to be a...which is 8.... times 55...

So we've got this positive time of 14.89 second

And you get s cosine of theta is equal to the horizontal component.

I'll just write it all in green, is going to be equal to v sub i times t.

If x is equal to, I don't know, 7, (x 7) then x 5, is going to be equal to

The total displacement, I'll do that in purple, the total displacement is going to be equal to our average velocity while we're accelerating, times the difference in time, or the amount of time it takes us to accelerate.

I WlLL LEAVE IT UP TO YOU AS AN EXERClSE TO HOW FAST THlS IS IN KlLOMETERS PER HOUR

This isn't less than or equal to, so we're going to put a parentheses here.

So let's say if this is 1 meter, the force of compression is going to be K times 1, so it's just going to be K.

So if you, if you, the 3 would replace the x. So, f (3), so f (3) is equal to 3 plus 2, which equals 5, right?

And now we can solve for when the first and the second derivatives equal 0, and we'll have our candidate, well, we'll know our critical points, and then we'll have our candidate inflection points, and see if we can make any headway from there.

So I'm first going to add 1 2, which is the same thing as 4 8.

If we want to figure out time in the air, we know that displacement is equal to the initial velocity times time

So area 1 times distance 1 (this area times this distance) is going to be equal to this area times this distance (area 2 times distance 2).

and that gives us 806 m. So this displacement right over here is 806 m

So you get s sine of theta is equal to the vertical component of our velocity, s sine of theta.

Any x that satisfies either of these will make this entire expression equal 0.

So when x is equal to 0, y is equal to 1.

And I'm just gonna set it to zero, and I'm gonna do that before the loop starts running.

And so C is greater than or equal to 3, so it can be equal to 3, so I'll fill that in right over there. Let me do it in a different color.

16 1 is 15, minus 2 is 14, minus 3 is 13, minus 4 is 12.

So y is equal to 1 when x is 0.

So your initial velocity is going to be 0, and once again I'm going to use the convention that the direction of the vector is implicit.

Now, we also know the angular velocity, or the magnitude of the angular velocity, is equal to the magnitude of our velocity, or the speed of our object, divided by the radius of the circle that it is going around.

Then we're going to have a bunch of zeroes equaling some number, which tells us that there's no solution.

Well, xi just means any of these x's, and I'll write for i is less than or equal to 2 and greater than or equal to 1, and i is an integer.

It's equal to minus 1, or B is equal to 1 3.

If A is equal to 9, what is B equal to?

B is equal to 9 plus what is equal to 2?

So b is 1 and a is 3.

So, when x is 0, y is equal to 1.

So s is equal to distance, and then t is equal to time.

And now we will use that to prove that the limit as x approaches 0 of sine of x over x is equal to 1.