A one-sided limit is a concept in calculus that refers to the value that a function approaches as the input approaches a specific value from either the left or the right side. In other words, it is the value that the function gets closer and closer to, but may not actually reach, as the input approaches a certain point.
The one-sided limit of sin(x)/x at x=0 is equal to 1. This means that as the input (x) approaches 0 from either the left or the right side, the function sin(x)/x gets closer and closer to the value of 1.
The one-sided limit of sin(x)/x at x=0 can be calculated using the limit definition in calculus, which involves plugging in values that are very close to 0 (but not equal to 0) into the function and seeing what value the function approaches. In this case, as the values get closer and closer to 0, the function approaches the value of 1, indicating that the one-sided limit is equal to 1.
The one-sided limit of sin(x)/x at x=0 is important because it helps us understand the behavior of the function sin(x)/x near the point x=0. It tells us that as the input gets closer and closer to 0, the function gets closer and closer to the value of 1, which can be useful in various applications of calculus.
No, the one-sided limit of sin(x)/x at x=0 is equal to the two-sided limit. This is because the function sin(x)/x is continuous at x=0, meaning that the limit from the left side and the limit from the right side are equal to each other. Therefore, the one-sided limit and the two-sided limit are both equal to 1.