Unbounded Limits
Sometimes there are certain kinds of functions that move towards infinity. In such cases, the value of the limit goes up to infinite. For example, for function f(x) given below,
f(x) =
The limit for this function at x = 0,
Notice in the figure that the limit at x = 0 is unbounded and is going up to infinity. Such limits are called unbounded limits.
Estimating Limits from Graphs
The concept of limits has been around for thousands of years. Earlier mathematicians in ancient civilizations used limits to approximate the area of a circle. But the formal concept was not around till the 19th century. This concept is essential to calculus and serves as a building block for analyzing derivatives, continuity, and differentiability. Intuitively, limits give us an idea about the values function approaches at a particular value of x. Using this idea, limits can also be estimated to a certain extent just by looking at the graph. Let’s look at these ideas in detail.
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