Is my approach to finding the limit of trig functions correct?

  • Thread starter Thread starter jkristia
  • Start date Start date
  • Tags Tags
    Limit Trig
Click For Summary
SUMMARY

The discussion centers on evaluating the limit of the trigonometric function lim (x -> 0) of (sin 2x) / (sin 3x). The user successfully applies the technique of rewriting the limit into the form (sin x) / x, multiplying by appropriate factors to simplify the expression. The final result is confirmed as 2/3, demonstrating the correctness of the approach. An alternative method using L'Hospital's Rule is mentioned but deemed less elegant by the user.

PREREQUISITES
  • Understanding of trigonometric limits
  • Familiarity with the limit properties of sin(x)
  • Basic knowledge of L'Hospital's Rule
  • Experience with algebraic manipulation of limits
NEXT STEPS
  • Study the derivation of the limit lim (x -> 0) of (sin x) / x
  • Explore advanced applications of L'Hospital's Rule in calculus
  • Practice solving limits involving trigonometric functions
  • Review techniques for algebraic manipulation in limit problems
USEFUL FOR

Students studying calculus, particularly those focusing on limits and trigonometric functions, as well as self-learners seeking to enhance their understanding of limit evaluation techniques.

jkristia
Messages
54
Reaction score
0
I'm still trying to figure out how to do limits of trig functions and I would like to know if this is the correct approach. I know the answer is correct, but not sure if that is just a coincidence.

Homework Statement



lim (x -> 0) of (sin 2x) / (sin3x).

Homework Equations


The Attempt at a Solution



First I try to get the equation into the form (sin x) / x or x / (sin x)
so I multiply by

(x/x)(3/3)(2/2)

this gives me

(1/3)(3x/sin3x)(2/1)(sin2x/2x)

so I get
(1/3)(1)(2/1)(1) = 2/3

Is that the correct approach?
 
Physics news on Phys.org
Yes, it is :smile:

Edit : Another way to solve this would be the use of L'Hospital principle, but this method is more elegant, in my opinion.
 
Thank you very much for the quick reply.

I'm trying to do calculus as a selfstudy, and the L'Hospital is not mentioned until another 320 pages.
 

Similar threads

Can the limit of a quotient of trig functions approach a specific value?
  • · Replies 2 ·
Replies
2
Views
2K
How to Determine Correct Inverse Trig Angle?
  • · Replies 2 ·
Replies
2
Views
1K
Use Graph to Determine Limit: Calculating Limits with Piecewise Functions
  • · Replies 3 ·
Replies
3
Views
1K
Finding the limit using a trig identity
  • · Replies 5 ·
Replies
5
Views
2K
Find the Cartesian equation given the parametric equations
  • · Replies 6 ·
Replies
6
Views
1K
Calculating radius of gyration of plane figure about x-axis
  • · Replies 5 ·
Replies
5
Views
3K
Can this function still be a constant function?
  • · Replies 11 ·
Replies
11
Views
2K
Calculating Limits Using Properties
  • · Replies 4 ·
Replies
4
Views
2K
lim x-->0 ##\frac{x tan2x -2xtanx} {(1-cos2x)^2}##
  • · Replies 5 ·
Replies
5
Views
1K
Comparing Hyperbolic and Cartesian Trig Properties
  • · Replies 1 ·
Replies
1
Views
2K