phymatter said:
)It's usually called the "floor" function.phymatter said:
The limit represents the value that a function approaches as the independent variable approaches a specific value. In this case, the limit represents the value that the function (sin[x])/x approaches as x gets closer and closer to 0.
The limit can be evaluated using various techniques, such as substitution, factoring, or L'Hopital's rule. In this case, we can use the fact that sin(0) = 0 and the definition of the derivative to evaluate the limit as 1.
No, the limit may not always be defined. In this case, the limit is only defined when x approaches 0 from both sides, as sin(0) is undefined. If x approaches 0 from only one side, the limit will not exist.
No, the limit can only be taken at points where the function is defined. In this case, the limit of (sin[x])/x can only be taken at x = 0, as this is the only point where the function is defined.
The limit of (sin[x])/x is a fundamental concept in calculus and is used to calculate derivatives and integrals of trigonometric functions. It also has applications in physics and engineering, such as in the study of motion and waves.