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

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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.
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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
 
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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 $\displaystyle \lim_{x \rightarrow 0}$?
 

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