Linerization of square root of sin(2x)

In summary, the linearization of the square root of sin(2x) involves finding the first-order Taylor polynomial of the function expanded about a given point. This linear approximation uses the equation of tangent and is related to differential calculus.
  • #1
songoku
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325

Homework Statement


Find the linerization of square root of sin(2x)


Homework Equations





The Attempt at a Solution


I don't even know how to start. What is linearization?

Thanks
 
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  • #2
It's just coming up with a linear approximation for the function about some point, that is, finding the first-order Taylor polynomial of the function expanded about a given point.
 
  • #3
Assuming you want to use a linear approximation of the function for some x near a, the linearization is
f(x) [itex]\approx[/itex] f(a) + f'(a)(x - a)

That's what vela was talking about when he mentioned the first-order Taylor polynomial. The "linear" part means that x appears to the first power only -- no higher powers.

BTW, this really seems like a calculus problem, so you probably should have posted it in the Calculus & Beyond section.
 
Last edited:
  • #4
Hi vela and Mark

sorry I don't know that linearization is related to equation of tangent, so it's related to differential. thanks a lot !
 

Related to Linerization of square root of sin(2x)

1. What is the purpose of linerization of the square root of sin(2x)?

The purpose of linerization of the square root of sin(2x) is to simplify and approximate the function for easier analysis and calculation. This technique allows us to break down a complicated function into smaller, simpler components, making it easier to understand and manipulate.

2. How is the linerization of the square root of sin(2x) calculated?

The linerization of the square root of sin(2x) is calculated using the Taylor series expansion, which involves taking the derivatives of the function at a given point and plugging them into a formula to find the approximation at that point.

3. What is the significance of the square root in the linerization of sin(2x)?

The square root in the linerization of sin(2x) is significant because it represents the inverse of the square function, which is commonly used in mathematical models and calculations. It allows us to approximate the function without losing significant accuracy.

4. Can linerization be applied to other trigonometric functions?

Yes, linerization can be applied to other trigonometric functions such as cosine, tangent, and their inverse functions. However, the specific technique and formula used may differ depending on the function.

5. How does linerization help in real-world applications?

Linerization of the square root of sin(2x) and other functions is used extensively in real-world applications, especially in fields such as physics, engineering, and economics. It helps in simplifying complex mathematical models and making accurate predictions and calculations, making it a valuable tool in many industries.

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