Find limits of sine and cosine functions

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Homework Help Overview

The problem involves finding the limit of the expression (1-cos2x)/(xsinx) as x approaches 0. The subject area relates to limits in calculus, particularly involving trigonometric functions.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to simplify the limit expression but arrives at a result of 2, which they believe is incorrect. Some participants affirm the result of 2 and question the validity of the original expectation that the limit should be 0.

Discussion Status

The discussion appears to have reached a point where multiple participants agree on the limit being 2, suggesting that the original poster may have misunderstood the problem or that there may be an error in the source material they referenced.

Contextual Notes

There is mention of a potential textbook error regarding the expected limit value, which may influence the understanding of the problem.

Glissando
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Homework Statement


Find the limit:

lim (1-cos2x)/(xsinx)
x->0


Homework Equations


Identities


The Attempt at a Solution



I've done this over and over and over again! The answer is supposed to be 0 but I keep getting 2 ):

lim (1-cos2x)/(xsinx)
x->0

lim (1-1+2sin2x)/(xsinx)
x->0

lim (2sin2x)/(xsinx)
x->0

lim (2sinx)/x
x->0

= 2*1 = 2

Any help is appreciated! Thank you!
 
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I don't see anything wrong with what you did. I'd say the limit is 2 as well.
 
Thanks guys (: I guess textbook error then! Yay!

Thank you <3
 

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