Let me draw my function.

So how could I construct this function right here using my unit step function?

So let me redraw my function here.

Now what is the range of my function?

They're saying you give me any x and you input it into my function of g and my function g will output

So say some constant, c1, times my first function, f of t, plus some constant, c2, times my second function, g of t.

Let's draw my position as a function of time.

Welcome to my presentation on domain of a function.

Let's say my function looks something crazy like that.

In fact, I respect my self and its function.

Times the Laplace transform of my derivative plus my function evaluated at 0.

I now resume my function as President of the Council.

I now resume my function as President of the Council.

So what happens if I input 4 into my function?

So if I define my function here, will this work?

He had some minor function on my staff in Cairo.

That blows my mind that it's a function where the slope at any point on that line is equal to the function.

Now my question to you is, can this function ever equal 0?

That was part of my function definition, I said we're mapping from R2, so my domain is R2.

So let's say that I have the second derivative of my function y plus 4 times my function y is equal to sine of t minus the unit step function 0 up until 2 pi of t times sine of t minus 2 pi.

So given that I was able to find for my function f, I was able to find a function that these two things are true.

So what if I my new function, I call it the unit step function up until c of t times f of t minus c?

Form is function. Form is function.

When I multiply this thing times my little delta function there, I get this.

And my function g essentially maps any point over here to exactly the point 2.

And then my function tells me that this will map to the point in R3.

So let's say I have my Dirac delta function and I'm going to shift it.

So it's this constant times my Dirac delta function, times delta of t minus c.

Function

Function

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Function

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Function

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Function

And so the answer to my problem is going to be the unit step function I just throw the 2 out there the 2 times the unit step function times my f of t shifted by c.

So what is the limit as tau approaches zero of my little d sub tau function?

Wish function

User function