The discussion revolves around evaluating a limit as x approaches 0, specifically involving the substitution u = x^2. Participants are trying to understand the implications of this substitution in the context of a limit problem presented in a math exam.
Some participants have suggested that using the substitution u = x^2 is beneficial for simplifying the limit expression. There is acknowledgment of the complexity of the limit, and while some guidance has been offered, there is no explicit consensus on the correct approach or interpretation of the problem.
Participants note the potential ambiguity in the problem statement and express uncertainty about how to derive the limit value of 4/5 from the given expressions. There is also mention of using L'Hôpital's rule, but the effectiveness of this method is still under discussion.
QuarkCharmer said:Is that sin(2x^2), sin^2(2x), sin(2)x^2 ?
Dick said:Or is it 3sin(2x^2-6x^2+4x^6)? The question isn't very grammatical. And however I rearrange it I still can't figure out how to pull 4/5 as a limit out.
vela said:It helps to use the substitution u=x2 to get
[tex]\lim_{u \to 0}\frac{3 \sin 2u - 6u + 4u^3}{u^5}[/tex]Then three applications of the Hospital rule gets you to a limit you can evaluate.