Practical Problems Involving Differentiation/Integration/Limits

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In summary, a person who struggled with learning differentiation, integration, and limits in their undergraduate course is seeking "real life" examples to better understand these concepts. They are asking for recommendations for simple, applicable problems that require differentiation and integration to solve. While there are thousands of examples available, most are in the realm of science and physics. The person suggests searching for examples related to work, acceleration, and geometry to find more relatable applications of these mathematical concepts.
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Crabman
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Hi guys,

As somebody who likes to learn and understand everyday problems I've really hit a wall...

I learned differentiation, integration and limits in my undergrad course, passed the exams etc but the way it was taught was pretty bad, nobody ever gave us "real life" examples. Personally I find that I learn much better with real life examples and so I thought I'd post here for some advice.

The real question is: Could you point me in the direction of some "real life" (simple, applicable problems) which require differentiation/integration to solve?

I know that there must literally be thousands and thousands but any help is appreciated.

Many thanks...
 
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Crabman said:
I know that there must literally be thousands and thousands but any help is appreciated.
Thousands of examples, yes. Everyday examples, no. You don't need differentiation or integration at the bakery around the corner. In science, however, and especially in physics it is daily business and examples can be found for any quantity which is defined as an integral, which solves a differential equation, or which is a derivative itself. So basically any physical quantity!

As I don't think those examples are meant I refrain from listing them. Google "work + example" or "acceleration + example" for those. Maybe geometric examples like the volume of rotation objects or path lengths is closest as you can get for "everyday" examples.
 

1. What is the difference between differentiation and integration?

Differentiation is a mathematical operation that essentially finds the rate of change of a function at a given point. It is represented by the derivative of the function. Integration, on the other hand, is the inverse operation of differentiation and involves finding the area under a curve represented by a function. It is represented by the integral of the function.

2. How are differentiation and integration used in practical problems?

Differentiation and integration are used to solve a wide range of practical problems in various fields such as physics, engineering, economics, and statistics. For example, in physics, differentiation is used to find velocity and acceleration, while integration is used to find displacement and work done. In economics, differentiation is used to find marginal cost and marginal revenue, while integration is used to find total cost and total revenue.

3. What are limits and why are they important in differentiation and integration?

Limits are a fundamental concept in calculus that describes the behavior of a function as the input approaches a certain value. In differentiation, limits are used to define the derivative of a function, while in integration, limits are used to determine the bounds of the integral. Limits are crucial in calculus as they allow us to understand the behavior of a function and make accurate calculations.

4. What are some common practical applications of differentiation?

Some common practical applications of differentiation include optimization problems, such as finding the maximum or minimum value of a function, and curve sketching, where we use the derivative to determine the shape of a curve. Differentiation is also used in physics to analyze motion and in economics to find the elasticity of demand.

5. How do you know when to use differentiation or integration in a problem?

Knowing whether to use differentiation or integration in a problem depends on the type of information given and the type of information needed. If the problem involves finding a rate of change, such as velocity or marginal cost, differentiation is used. If the problem involves finding the total amount, such as displacement or total cost, integration is used. It is important to understand the problem and what information is being asked for to determine which operation to use.

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