So, the limit of our function is the value of y as x gets closer to 9. In our domain, 9 is the highest value x can be. If that doesn’t make sense, think of it this way: The limit is the value that y approaches as x approaches a given value. It’s just a more natural way of writing it, so you don’t have to list every number in the set. The ellipsis (…) indicates that all numbers in between 3 and 9 are included in the domain. While the domain can be essentially infinite, for our purposes, we will create a relatively small domain.įor our little function, we’ll say that x can be The domain of an equation or function is a set of all the possible values of the independent variable (x) that will produce a valid dependent variable (y). ![]() The value of the independent variable always determines the value of a dependent variable. ![]() The value of y will change depending on the value of (x), the independent variable. Dependent VariablesĪ dependent variable is whatever value is yielded by the function, represented in our example as y. It’s a number that you’re plugging into the function to change the output. A function is typically notated like this: f(x) = y, though there’s usually much more to it than that.įor an equation to be a function, any number you plug in as the (x) variable has to cause the equation to equal precisely one value of y.Īn independent variable is a value of (x) in a function. You’ve probably already covered functions in advanced algebra or trigonometry, so we’ll just do a quick review. Differentiation was then generalized to Euclidean space and the complex plane. In the 19th century, calculus became more rigorous by those such as Bernhard Riemann, Augustin Louis Cauchy, and Karl Weierstrass. Many other mathematicians have contributed to the differentiation theory since the 17th century. The main insight that earned them the accreditation of calculus is due to the fundamental theorem of calculus relating differentiation and integration. The modern-day calculus development is generally credited to Isaac Newton and Gottfried Wilhelm Leibniz who provided different approaches to differentiation and derivatives. If you wanted to know precisely how fast you were going at any given second, you’d need to use calculus to figure it out.īefore we can explain how to do that, we need to define some of the terms you’ll use in calculus so you can follow along with our basic guide to differential calculus.ĭifferentiation dates all the way back to the Greek era, such as Euclid, Archimedes, and Apollonius of Perga. It works fairly quickly, but it’s not instant. Your odometer gives you an estimate of how fast you’re driving, based on the distance you’ve travelled over the past few seconds. So, what does that mean? We’ll use the speed of a car as an example. ![]() Differential calculus looks at the instantaneous rate of change. What is Differential Calculus? Photo credit to YouTubeĬalculus is a branch of math that’s focused on the study of continuous change. Once you’ve mastered the basics, you’re ready to take on more challenges. Whether you’re preparing for an upcoming semester of calculus class, or you’re looking for some extra help understanding what you’ve been learning, our basic guide to differential calculus can help. ![]() The good news is, calculus isn’t as complicated as it seems, as long as you have a strong background in algebra, trigonometry, and geometry. Unless you’re a math genius, you’re probably quite intimidated by calculus.
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