MHB One-Sided Limit of Sin(x)/x at x=0

  • Thread starter Thread starter spartas
  • Start date Start date
  • Tags Tags
    Limits
Click For Summary
The discussion focuses on finding the one-sided limit of the function f(x) = sin(x)/x for x > 0 and f(x) = x + 1 for x ≤ 0 at x = 0. The squeeze theorem is suggested as a method to solve the limit for the first part. It highlights that as x approaches 0, cos(x) approaches 1, indicating that sin(x)/x also approaches 1. For the left side, as x approaches 0 from the left, f(x) approaches 1. Therefore, the one-sided limit at x = 0 is confirmed to be 1.
spartas
Messages
7
Reaction score
0
find the one sided limit at the point x=0 for functions

f(x)={ sinx/x, x greater than 0 ; x+1, x less or equal than 0
 
Mathematics news on Phys.org
Hi spartas,

The first limit can be solved using "the squeeze theorem". Here is a hint.
$$ \cos(x) < \frac{\sin(x)}{x} < 1 $$
What happens to the left and right sides for $\displaystyle \lim_{x \rightarrow 0}$?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Undergrad Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
  • · Replies 16 ·
Replies
16
Views
1K
High School Proof of Chain Rule: Understanding the Limits
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad My attempt to understand horizontal transformations of functions
  • · Replies 6 ·
Replies
6
Views
2K
MHB Is this Trigonometric Expression a Constant Function of x?
  • · Replies 2 ·
Replies
2
Views
1K
MHB Finding the domain of this function.
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Limit of ##i^\frac{1}{n}## as ##n \to \infty##
  • · Replies 14 ·
Replies
14
Views
2K
High School Can We Simplify the Taylor Series Expansion for e^(f(x,y))?
  • · Replies 3 ·
Replies
3
Views
2K
Calculate the limit cos(x)/sin(x) when x approaches 0
  • · Replies 12 ·
Replies
12
Views
3K
MHB High school inequality |(√(sinx)+1)^2−(√(sina)+1)^2|<b
  • · Replies 4 ·
Replies
4
Views
2K
High School What Are Basic Questions About Understanding Inequalities?
  • · Replies 12 ·
Replies
12
Views
2K