[ASK] Limit of Trigonometry Function

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Discussion Overview

The discussion revolves around evaluating the limit of a trigonometric function as \( x \) approaches 0. Participants explore methods such as substitution and L'Hôpital's rule to simplify the expression and determine a numerical result.

Discussion Character

  • Mathematical reasoning, Technical explanation

Main Points Raised

  • One participant presents a limit expression involving sine functions and notes that direct substitution leads to an indeterminate form of \( \frac{0}{0} \).
  • Another participant suggests that L'Hôpital's rule can be applied repeatedly until the indeterminate form is resolved.
  • A later reply claims that after applying L'Hôpital's rule to the third derivative, the result simplifies to \( \frac{4,608}{24} \), which equals 192.
  • There is a confirmation of the previous claim regarding the result being 192.

Areas of Agreement / Disagreement

There appears to be a consensus on the application of L'Hôpital's rule and the resulting value of 192, although the method to reach this conclusion is not fully detailed.

Contextual Notes

The discussion does not clarify the assumptions made during the application of L'Hôpital's rule or the specific steps taken to arrive at the third derivative.

Monoxdifly
MHB
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$$\lim_{x\to0}\frac{sin2x+sin6x+sin10x-sin18x}{3sinx-sin3x=}$$
A. 0
B. 45
C. 54
D. 192
E. 212

Either substituting or using L'Hopital gives $$\frac00$$. Is there any way to simplify it and make the result a real number?
 
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We can repeat L'Hôpital until it's not $\frac 0 0$ any more.
 
Ah, I see. It's in the third derivative and the answer is $$\frac{4,608}{24}$$= 192, right?
 
Monoxdifly said:
Ah, I see. It's in the third derivative and the answer is $$\frac{4,608}{24}$$= 192, right?
Yep. (Nod)
 

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