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

  • Thread starter Thread starter spartas
  • Start date Start date
  • Tags Tags
    Limits
AI Thread 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 $\displaystyle \lim_{x \rightarrow 0}$?
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Back
Top