Understanding the Limit of Sin7x/4x as x Approaches 0

Click For Summary
SUMMARY

The limit of sin(7x)/4x as x approaches 0 is evaluated using the fundamental limit property that states lim x→0 (sin x)/x = 1. By substituting 7x for x in this property, we find that lim x→0 (sin(7x))/(7x) = 1. Consequently, the limit can be expressed as lim x→0 (sin(7x)/4x) = (7/4) * lim x→0 (sin(7x)/(7x)) = 7/4.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with trigonometric functions
  • Knowledge of the limit property lim x→0 (sin x)/x = 1
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the derivation of the limit property lim x→0 (sin x)/x = 1
  • Explore L'Hôpital's Rule for evaluating indeterminate forms
  • Learn about Taylor series expansions for trigonometric functions
  • Investigate the application of limits in real-world scenarios
USEFUL FOR

Students studying calculus, educators teaching limit concepts, and anyone looking to deepen their understanding of trigonometric limits.

Coldie
Messages
84
Reaction score
0
You're asked to find lim x-->0 sin7x / 4x

The part of this example that I don't understand the most is how they get 1 out of sin7x/7x when x-->0.

[edit]
Sorry about the ridiculously small image. The dimension restrictions are ridiculous, and I didn't notice that the image didn't attach properly the first time.
[/edit]
 

Attachments

  • calc1.jpg
    calc1.jpg
    9.3 KB · Views: 529
Last edited:
Physics news on Phys.org
Are you familiar with [itex]\lim_{x \rightarrow 0} (sin x) / x = 1[/itex]?
 
No, I was not. I guess that clears that up, thanks:p
 

Similar threads

Undergrad Proof of 1/(x^2) Not Having Limit at 0
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad The Basic Area Problem (introduction to the topic of integrals)
  • · Replies 24 ·
Replies
24
Views
4K
High School Nature of Limits: Learn Calculus Basics w/o Limits Distraction
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad Understanding Limits - Spivak Calculus
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Understanding a Step in Finding a Limit: Lim(x->0) x.sqrt(x+2) / sin(x)
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Differentials of order 2 or bigger that are equal to 0
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Understanding Calculus Theorems for Limits
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad What Is g(x) in the Limit as x Approaches 3?
  • · Replies 3 ·
Replies
3
Views
5K
Undergrad How to understand the notion of a limit of a function
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Extremal condition in calculus of variations, geometric
  • · Replies 7 ·
Replies
7
Views
3K