Estimating Limits from Graphs
Consider the function f(x),
f(x) = 3x + 4
This is an equation of a line. Let’s see what the value of the limit of this function at x = 1 is. The figure below shows the graph for this function,
Notice that as we approach from both the left-hand side and right-hand side of x = 1, the function moves toward a single value. This value is called the limit of the function.
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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