The "importance" of Limits Hey, I am a student in the physics and engineering fields. I have been doing calculus for two years. I understand that the limit is, in a sense, the "building block" of calculus. Differentiation and the derivative is defined by calculating the difference quotient Δy/Δx of a function and taking the limit as Δx approaches 0. Definite integration involves finding the area of the region under a function using n number of rectangles and letting n approach infinity. Again, I understand that limits are important because they are framework for calculus. Finding the derivative of a function using the limit process is great for demonstrating the nature of differentiation, but this can be a tedious process. There are proven methods for computing derivatives; There is the power rule, product and quotient rules, the chain rule, all based on the properties of limits. Finding the area underneath a function using the limit process, again shows how the area can primitively be solved. Needless to say, this is also a tedious (and paper consuming) process. Use the FTC or integration by substitution/parts. Is it vitally important to memorize the properties of limits themselves? Learning them initially was great; they were intuitive and simple to understand, but when I ventured into the deeper parts of calculus, I found myself having to, every now and then, review seeming useless theorems and rules. After a while, limits just seem to be a waste of memory. I mean is it extremely likely that in the "real" world of physics that you foul up terribly because you forgot about the Squeeze Theorem? When will I actually have to compute or work with a limit directly?