A limit of a function is the value that a function approaches as its input approaches a certain value. It represents the behavior of the function near a specific input value.
To find the limit of a sine function, you can use the fact that the limit of sin(x) as x approaches a value a is equal to sin(a). In other words, the limit of sin(x) as x approaches a is equal to the value of the sine function at a.
Yes, the limit of a sine function can be undefined. This can happen when the function has a vertical asymptote (a point where the function approaches infinity) or a jump discontinuity (a point where the function has a sudden change in value).
Similar to the sine function, the limit of a cosine function can be found by simply plugging in the value that the function is approaching. So the limit of cos(x) as x approaches a is equal to cos(a).
The left limit of a function at a specific point is the value that the function approaches as the input approaches that point from the left side. The right limit is the value that the function approaches as the input approaches from the right side. If the left and right limits are equal, then the overall limit exists. If they are not equal, then the limit does not exist.