The number of points of where limit of f(x) does not exist is : (A) 3 (B) 4 (C) 5 (D) None of th

step 1 Hello everyone we are going to solve a question in this question we are given a function fx is e

The number of points of where limit of f(x) does not exist...

Key Concepts

Limit of a Function

This concept involves understanding the behavior of a function as the input approaches a specific point. A limit exists if the values of the function get arbitrarily close to a particular number from both sides. If the left-hand limit and the right-hand limit at that point differ, or if the function does not settle at one value, the limit does not exist.

Points of Discontinuity

Points of discontinuity refer to values in the domain of a function where the function is not continuous. Discontinuities can occur for various reasons including jumps, holes, or vertical asymptotes. At these points, the limit of the function may fail to exist because the behavior on either side of these points is not compatible with smooth, continuous progression.

Jump Discontinuity

A jump discontinuity occurs when the left-hand and right-hand limits at a point both exist but are not equal. This is a typical example of a situation where the overall limit does not exist at a specific point. Analysis of such points is crucial in understanding the overall behavior of a function.

Analysis of Piecewise Functions

In piecewise defined functions, different formulas apply to different intervals of the domain. The boundaries where the function's rule changes are common places for discontinuities. Evaluating the limits at these boundaries involves checking the behavior of the function from both sides to decide if the limit exists or if there is a discontinuity.

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