Linear Approximation: Intro to Physics Problem

In summary, linear approximation is a useful tool in physics for estimating the value of a function at a certain point by using the tangent line. It simplifies complex equations and is commonly used in situations where the exact value is difficult to calculate. The steps involved include choosing a point, finding the slope of the tangent line, and substituting the value of x into the equation. It has various applications in physics, such as estimating velocity and force, but it may not provide accurate results for highly curved or nonlinear functions. Additionally, the accuracy may decrease as the distance from the point of approximation increases.
  • #1
karush
Gold Member
MHB
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https://www.physicsforums.com/attachments/1614
never done this before so this is an intro problem
it mentioned that LA is used in Physics a lot
hopefully correct no ans in bk(Speechless)
 
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  • #2
karush said:
https://www.physicsforums.com/attachments/1614
never done this before so this is an intro problem
it mentioned that LA is used in Physics a lot
hopefully correct no ans in bk(Speechless)
Looks good to me.

-Dan
 
  • #3
I post a couple more...
 

FAQ: Linear Approximation: Intro to Physics Problem

What is linear approximation in physics?

Linear approximation is a method used to estimate the value of a function at a certain point by using the tangent line at that point. It is a useful tool in physics because it allows us to simplify complex equations and make approximations that are close enough to the exact values for practical purposes.

How is linear approximation used in physics?

Linear approximation is used in physics to simplify complex equations and make approximations that are close enough to the exact values for practical purposes. It is often used in situations where the exact value of a function is difficult or time-consuming to calculate.

What are the steps involved in linear approximation?

The steps involved in linear approximation are as follows:
1. Choose a point (x=a) to approximate the function.
2. Find the slope of the tangent line at that point.
3. Write the equation of the tangent line in the form y = mx + b.
4. Substitute the value of x into the equation to find the approximate value of the function at that point.

What are some common applications of linear approximation in physics?

Linear approximation is commonly used in physics to estimate values such as velocity, acceleration, and force in situations where the exact values are difficult to calculate. It is also used in the study of oscillations, thermodynamics, and electric circuits, to name a few.

What are the limitations of linear approximation in physics?

Linear approximation is based on the assumption that the function is approximately linear near the point of approximation. Therefore, it may not provide accurate results if the function is highly curved or nonlinear. Additionally, the approximation may become less accurate as the distance from the point of approximation increases.

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