micromass said:
KiwiKid said:
micromass said:
A limit is a fundamental concept in calculus that represents the value that a function approaches as the input value goes towards a specific point.
Finding the value of a limit allows us to understand the behavior of a function near a specific point and make predictions about its behavior at that point.
To find the value of a limit, we can evaluate the function at values closer and closer to the specific point in question until we can determine the value that the function approaches.
A left-sided limit looks at the behavior of a function as the input value approaches the specific point from the left side, while a right-sided limit looks at the behavior as the input value approaches from the right side. The two-sided limit considers both approaches simultaneously.
All continuous functions have limits, but not all limits exist. Limits may not exist if the function has a vertical asymptote or if it has a jump discontinuity at the specific point in question.