Can any of you think of a job that uses limits in Calculus? Sources would be niec if you can provide them.?

Question

a job that depends on or uses limits or just a practical use of limits or a real life application.

Answer 1

When you approach a point of dimensioning returns you are approaching a limit. Currently the speed of light is an absolute limit that can't be reached or surpassed. However, other machines from incandescent light bulbs, to car engines, to solar cells, to motors have a limit on their function. If you increase the size or the fuel, or add gears you can increase the function but you still reach ultimate limits.

The incandescent light bulb generates more heat than light and is only 40% efficient while the LED (light emitting diode) is over 90% efficient. The internal combustion engine is only about 40% efficient, but the efficiency has been improved by switching to aluminum engine blocks. Power has been increased by using fuel injection and computer timing. All of these are limits and when the engineers try to improve the function of the machine they do it with math; physics, hydrodynamics, thermodynamics and calculus.

If you want to improve the efficiency of a fuel injection system then you can increase the air pressure or the fuel supply, or the efficiency of the spark plug. When calculating how far to go the company will have the engineers increase the efficiency until it approaches a limit that makes it more expensive. An increase of 20% is worth 75$, but an increase of an extra 10% is not worth $200. Unless you are designing a race car; then you have the engine blueprinted, using tighter tolerances you make a better engine, but you increase the cost.

The engineer won't always calculate the limit, but if they develop a function for their machine then they look for the limit. If torque X air flow / size = a certain value then that function will have a limit on it, unless it can be continually increased without a problem. Realistically though the machine will leave that formula at a certain point and it can't be improved any more.

Steel and other construction materials have a limit on their strength; with metals there is a plastic range where the item deforms. When you are designing a metal bracket you need to keep it as thin as possible to save weight and cost; but you need to take it to a point below the limit of the metal’s strength. I don’t mean the physical limit; I mean the limit of the function as it describes the strength of the material as stress on it increases. The graph goes up along a certain pattern and it has a limit to the maximum strength. As an engineer I want to know how strong the metal brackets are and I don’t want to have to test them every time I design a new bracket. I want a math formula that tells me how strong it will be for a specific size, under a certain load. As the load changes the stress changes and the bracket is pulled toward its breaking point. I need to design in a safety factor and I need to know how close I can get to the function’s limit to figure out how far I can push it.

Limits are an important, but difficult concept in calculus. One bad thing about school is they don't teach you just how useful math is. ALL of Engineering is based on physics and that requires calculus. If you want to figure out the volume of an irregular container; like a coca cola bottle; then you need calculus. Part of the bottle is a curve that has a formula that approaches a limit, you take a sum of the different parts of the bottle and often they are not regular spheres and rectangles. To figure out the volume they need to know the formula (the function) for each part of the container.

It is a pain in the rear to find out that ALL engineers and scientists need to know calculus to use the formulas of their work; or at least know it to learn where those formulas came from. Then you find out that physics runs through those fields like a huge river. It connects them, it is needed by them, and it changes oddly like a river can.