Notice in the figure that the limit at x = 0 is unbounded and is going up to infinity. For example, for function f(x) given below, In such cases, the value of the limit goes up to infinite. Sometimes there are certain kinds of functions that move towards infinity. This value is called the limit of the 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. The figure below shows the graph for this function, Let’s see what is the value of the limit of this function at x = 1. The graphical method simply involves making a graph of the function and then the limit can be estimated just by looking at the graph. Limits to any function can be calculated two approaches:Īlgebraic methods involve manipulating the function such that its limit can be calculated easily. If f(x) has different right and left limits, then the two-sided limit ( ) does not exist. If f(x) never approaches a specific finite value as x approaches c, then we say that the limit does not exist. If the limit of f(x) as x approaches c is the same from both the right and the left, then it is said the limit of f(x) as x approaches c is L.If f(x) gets closer and closer to a specific value L as x approaches a chosen value c from the left, then it is said that the limit of f(x) as x approaches c from the left is L.If f(x) gets closer and closer to a specific value L as x approaches a chosen value c from the right, then it is said that the limit of f(x) as x approaches c from the right is L.Similarly, right-hand limit is denoted as, Average and Instantaneous Rate of Change.Class 11 NCERT Solutions - Chapter 3 Trigonometric Function - Exercise 3.1.Class 11 NCERT Solutions - Chapter 7 Permutations And Combinations - Exercise 7.1.Difference Between Mean, Median, and Mode with Examples.
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