Question

Find example in which limₜ→[infinity] ∅(t) = x⁰ but x⁰ not stable not stable

Answer 1

In mathematics, the limit of an empty set or a function with no values in its domain as t approaches infinity can have a certain value x⁰. However, x⁰ may not be a stable value if the function does not approach it from both sides. An example of this is the function y = sin(t), where as t goes to infinity, the function oscillates between -1 and 1 without settling on a particular value.

Step-by-step explanation:

In mathematics, the symbol ∅(t) represents an empty set or a function that has no values in its domain. In this case, we are looking at the limit as t approaches infinity. When
`limₜ→[infinity] ∅(t) = x⁰`larger and larger, the function approaches a certain value x⁰. However, if x⁰ is not a stable value, it means that the function does not approach it from both sides as t goes to infinity.

An example of this would be the function y = sin(t), where t is an angle in radians. As t approaches infinity, the function oscillates between -1 and 1, never settling on a particular value. Therefore,
`limₜ→[infinity] sin(t)` value.