Linerization of square root of sin(2x)

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Homework Help Overview

The discussion revolves around the linearization of the square root of the sine function, specifically sin(2x). Participants are exploring the concept of linear approximation in the context of calculus.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about the concept of linearization and how to begin the problem. Some participants clarify that linearization involves finding a linear approximation of a function near a specific point, referencing the first-order Taylor polynomial. Others note the connection between linearization and the equation of a tangent line.

Discussion Status

The discussion is active, with participants providing clarifications about linearization and its relation to calculus concepts. There is no explicit consensus, but helpful guidance has been offered regarding the nature of linear approximations.

Contextual Notes

One participant suggests that the problem may be more appropriately categorized under calculus topics, indicating a potential misplacement in the forum structure.

songoku
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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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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.
 
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:
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 !
 

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