PROFESSOR: Hi. Well, this is exponential day, the day for the function that only calculus could create, y is e to the x. And it couldn’t have come from algebra because, however we approach e to the x, there’s some limiting step. Something goes to 0. Something goes to infinity. I’ve got different ways to…

# Tag: calculus

## Graphing Functions and Their Derivatives

Professor Dave here, let’s get back to graphing. I’m sure you got enough of graphing when we learned algebra, but we need to expand our abilities now that we understand differentiation. First, as we recall, the derivative of a function at a particular point is equal to the rate of change in the function at…

## What are some real-world examples of functions? – Week 1 – Lecture 4 – Mooculus

[MUSIC] So, there’s all these different ways of taking two functions and producing new functions. You could add, subtract, multiply, divide two functions, and could take two functions and compose them, meaning that the output for the one becomes the input for the other. In light to this, I’d encourage you just to pick up…

## Ex: Determine the Velocity Function and Acceleration Function from the Position Function

– THE FOLLOWING FUNCTION GIVES THE HEIGHT OF A PROJECTILE IN METERS AFTER T SECONDS. WE WANT TO DETERMINE THE HEIGHT, VELOCITY, AND ACCELERATION AFTER THREE SECONDS. BEFORE WE DO THIS, LETS TAKE A LOOK AT THE GRAPH OF THIS FUNCTION. WE’VE ALREADY TYPED IN THE FUNCTION INTO Y1 AND I’VE ALREADY ADJUSTED THE WINDOW…

## Differentials of Functions of Two Variables

– WELCOME TO A LESSON ON DIFFERENTIALS FOR FUNCTIONS OF TWO VARIABLES. IN CALCULUS ONE WE LEARNED THAT FOR FUNCTIONS OF ONE VARIABLES DIFFERENTIAL Y OR DY WAS EQUAL TO F PRIME OF X x DX. WELL, FOR FUNCTIONS OF TWO VARIABLES, MEANING Z IS DEFINED IN TERMS OF X AND Y, X AND Y…

## Optimizing Functions of Two Variables

In this video, we’re going to work a few optimization problems for functions of several variables. So before we do a specific problem, let’s review the strategy. We want to find local extrema, so if we have a function of two variables, you compute the partial derivatives and you either see where they don’t exist…

## Limits Involving Absolute Value Functions Calculus 1 AB

I am mr. Tarrou. In this calculus lesson we’re gonna be doing two examples of finding limits of functions that involve absolute value functions within them this is going to be a continuation of course of us finding limits using properties of limits if you want more examples there’ll be a link in the description…

## MOOCulus: Episode 1 – What are functions?

calculus studies functions and this course is no exception, we’re going to be studying functions in this course, alright… functions like f(x) or the sine function or the square root function and that raises a question… what are functions? if we’re gonna be studying functions we should know what they are that question is pretty…