Limits can exhibit different behaviors depending on the properties of the function being analyzed. Here are three important types of limits:

1. One-Sided Limits: A one-sided limit is evaluated when the function approaches a specific value from either the left or the right.

Example:

For the function f(x) = |x|, as x approaches 0 from the left (denoted as x → 0^-), the limit is -1. However, as x approaches 0 from the right (denoted as x → 0^+), the limit is 1.

2. Infinite Limits: An infinite limit occurs when the function approaches positive or negative infinity as the input approaches a certain value.

Example:

Consider the function f(x) = 1/x. As x approaches 0, the limit is ∞ because the function's values become arbitrarily large as x gets closer and closer to 0 from either side.

3. Limits at Infinity: A limit at infinity is evaluated when the input approaches positive or negative infinity.

Example:

For the function f(x) = 1/x, as x approaches positive infinity (denoted as x → ∞), the limit is 0, indicating that the function's values become arbitrarily close to 0 as x grows infinitely large.

Explore these different types of limits to gain a more comprehensive understanding of the behavior of functions!