The reason why lim(x-->0) cos(1/x) does not exist is because the function cos(1/x) oscillates infinitely as x approaches 0. This means that the values of the function keep changing rapidly and do not approach a single, finite value. As a result, the limit of the function at x = 0 does not exist.
Yes, an example of lim(x-->0) cos(1/x) not existing is when x takes on values that are very close to 0, such as 0.001, 0.0001, 0.00001, and so on. As x gets closer to 0, the values of cos(1/x) will keep oscillating between -1 and 1, never approaching a single value.
No, since the limit of cos(1/x) does not exist, there is no way to determine its value at x = 0. This is because the values of cos(1/x) keep changing rapidly and do not approach a single, finite value.
No, the limit of a function not existing does not necessarily mean that the function is undefined at that point. In this case, cos(1/x) is defined for all values of x, including 0. It is just that the limit of the function at x = 0 does not exist.
No, graphing the function cos(1/x) will not provide any information about its limit at x = 0. This is because the graph would show the oscillations of the function, but it cannot determine the exact value of the limit at x = 0. A limit can only be found using analytical methods, such as algebraic manipulation or using the definition of a limit.