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. 

Similar Reads

Limit

The limit of a function at a number x = a can be thought of as the value function starts to take while reaching towards x = a. The point x = a can be approached from either of the sides, the left-hand side or the right-hand side. For example, let’s consider a function f(x), then the limit of the function at x = a is denoted as,...

Estimating Limits from Graphs

Consider the function f(x),...

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,...

One-Sided Limits

Sometimes functions are not continuous, which means they tell us two different limits while approaching from two different sides. For example, the greatest integer function is inherently discontinuous, and at these discontinuities, we observe two different values....

Limits and Graphical Behavior

Limits can tell a lot about a function’s behavior at some particular point. Then how should one use it? In cases where it is known that the function is discontinuous, it becomes hard to analyze the graph of the function solely using derivatives. In such cases, limits can be used to find the values of the function at the points of discontinuities. For example, let’s say we have a function f(x),...

Solved Questions on Estimating Limits from Graphs

Question 1: Find the...

Contact Us