What is the limit of (sin2s)^4/s^4 as s approaches 0?

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Homework Help Overview

The discussion revolves around finding the limit of the expression (sin(2s))^4/s^4 as s approaches 0, which falls under the subject area of calculus, specifically limits and trigonometric functions.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the manipulation of the limit expression, considering the relationship sin(x)/x as x approaches 0. There is discussion about factoring constants out of the limit and how to properly express the function in a usable form.

Discussion Status

Some participants have provided insights into the limit properties of sine functions, and there is a suggestion of using the known limit sin(ax)/(ax) = 1. However, the discussion does not reach a consensus, as some participants are still grappling with the algebraic manipulation required.

Contextual Notes

Participants mention the need to manipulate the function into a specific form to apply known limit properties, indicating a potential challenge in the algebra involved.

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Homework Statement


Find the limit or prove it does not exist.

lim as s->0 (sin2s)^4/s^4


Homework Equations


i know i have to use sinx/x = 1 but I am having trouble manipulating the function into that form


The Attempt at a Solution



my first thought was that i could just take the 2 out as a constant would that just be (2^4)(sinx)^4/x^4

but then i have (sinx)^4 not sinX^4 I am stuck on what king of algebra will work here
 
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a^2/b^2=(a/b)^2
 
Lim_(x->0) of sin(ax)/(ax)=1
 
ahh so then (2*1)^4 = 16

thanks a lot
 
beneakin said:
ahh so then (2*1)^4 = 16

thanks a lot
good, welcome!
 

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