Question

What is an example of a situation where the limit doesn't exist?

1) The limit approaches infinity
2) The limit approaches negative infinity
3) The limit oscillates between two values
4) The limit does not approach a specific value

Answer 1

An example of a situation where the limit doesn't exist is when the limit oscillates between two values.

Step-by-step explanation:

An example of a situation where the limit doesn't exist is when the limit oscillates between two values. In this case, as the input approaches a certain value, the output keeps switching between two different values instead of converging to a specific value.

Answer 2

An example of a situation where the limit doesn't exist is when the limit oscillates between two values. Option C is answer.

Step-by-step explanation:

A limit is said to exist if it approaches a specific value as the input approaches a certain point. However, if the limit oscillates between two values or does not approach any specific value as the input approaches a certain point, then the limit does not exist.

Here are some examples of situations where the limit doesn't exist:

The function f(x) = sin(x)/x, as x approaches 0: The function oscillates infinitely between 1 and -1 as x approaches 0, and it does not approach any specific value. Therefore, the limit does not exist.

The function f(x) = 1/x, as x approaches 0: The function approaches positive infinity as x approaches 0 from the positive side, and approaches negative infinity as x approaches 0 from the negative side. Since the limit approaches different values from different sides, the overall limit does not exist.

The function f(x) = |x|, as x approaches 0: The function changes direction abruptly at x = 0, making its limit undefined.

Therefore, when a function oscillates between different values or does not approach any specific value as the input approaches a certain point, we know that its limit does not exist.

Option C is answer.