Limit (sin(4x)/sin(6x)) as x->0

  • Thread starter Thread starter adamjts
  • Start date Start date
  • Tags Tags
    Limit
Click For Summary

Homework Help Overview

The discussion revolves around evaluating the limit of the expression (sin(4x)/sin(6x)) as x approaches 0, within the context of introductory calculus. Participants are encouraged to find a solution without employing L'Hospital's rule.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need to rewrite the limit expression in a form that allows the application of the known limit (sin(x)/x) as x approaches 0. There are attempts to manipulate the expression by factoring out terms related to sin(4x) and sin(6x). Some participants question the steps taken to arrive at the limit and suggest corrections to ensure proper application of the limit properties.

Discussion Status

The discussion is active, with participants exploring different approaches to solve the limit problem. Some guidance has been offered regarding the correct form needed to apply the limit, while others have reiterated the importance of not using L'Hospital's rule. There is a mix of interpretations regarding the steps to take, but no consensus has been reached on a final method.

Contextual Notes

Participants are reminded that the problem must be solved without using L'Hospital's rule, which has led to some confusion and varied approaches in the discussion.

adamjts
Messages
24
Reaction score
0
Hi all,

I'm just beginning calculus and I'm having trouble figuring this one out.

I need to solve this one without using l'hospital's rule.



Homework Statement



Find

Limit (sin(4x)/sin(6x)) as x->0

Homework Equations



We know that limit (sin(x)/x) as x -> 0 equals 1



Thanks! Much appreciated!
 
Physics news on Phys.org
adamjts said:
Hi all,

I'm just beginning calculus and I'm having trouble figuring this one out.

I need to solve this one without using l'hospital's rule.



Homework Statement



Find

Limit (sin(4x)/sin(6x)) as x->0

Homework Equations



We know that limit (sin(x)/x) as x -> 0 equals 1



Thanks! Much appreciated!

In order to use the limit you now, you must rewrite the expression so that you have a factor
\frac{\sin(4x)}{4x} right? And you need to rewrite the \frac{1}{\sin(6x)} in what form?
 
OH. so i'd go

= limit (sin(4x)/1) * Limit (1/sin(6x))

= Limit (4sin(4x)/4) * Limit (6/6sin(6x))

= 4/6

=2/3

Yeah?
 
adamjts said:
OH. so i'd go

= limit (sin(4x)/1) * Limit (1/sin(6x))

= Limit (4sin(4x)/4) * Limit (6/6sin(6x))

= 4/6

=2/3

Yeah?

Almost! You need to get \frac{\sin(4x)}{4x} in order to take the limit, not
\frac{\sin(4x)}{4}. And same thing for the sin(6x).So you need to correct one step. But your final answer is correct. Good job!
 
  • Like
Likes   Reactions: 1 person
This can be done by
L HOSPITAL's rule
 
Differentiate with respect to x on denomenator and numerator and you get the answer
 
Ans is 2/3
 
Midhun said:
This can be done by
L HOSPITAL's rule

The question asks to NOT use L'Hospital's rule. Which is why I suggested this approach.
 

Similar threads

  • · Replies 12 ·
Replies
12
Views
4K
Replies
4
Views
4K
Replies
11
Views
2K
  • · Replies 18 ·
Replies
18
Views
2K
  • · Replies 13 ·
Replies
13
Views
13K
Replies
7
Views
2K
  • · Replies 15 ·
Replies
15
Views
7K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K