Question

What’s the difference between: undefined, does not exist and infinity?

Answer 1

Hint: Problems like these are quite easy to understand and simple to solve once we understand the underlying concepts behind the problem. To solve these types of problems effectively, we need to have some basic as well as advanced knowledge of calculus including limits, differentiation and continuity. To understand the difference between the given terms, we first of all need to know the definition of the terms. From the definition, we can easily figure out what is the difference between all of them.

Complete step by step answer:
Now we start off with the solution of the given problem by writing that, the definition of all the three terms are as follows,
Undefined: This situation occurs for a function when for a particular value of ‘x’ there is no corresponding value of ‘y’. We say that the function is not defined or undefined at that particular value of ‘x’. For example, $$y={\displaystyle \frac{1}{x-1}}$$ , here the function is not defined at $$x=1$$ .
Does not exist: This situation occurs when the limiting value at a particular point is not valid. In other words, the right hand limit and the left hand limit are not equal in this case.
Infinity: This situation occurs when the limit exists and the value of the limit is equal to infinity.

Note: Solving problems of these types requires a fair amount of idea of calculus such as limits, continuity and differentiability. We need to be very careful while evaluating the values of different limits in real problems. One term in the problem should not be confused with the other because it may lead to wrong answers in case of multiple choice questions. We should also remember that getting a limiting value equal to infinity is not equivalent to that of undefined or does not exist.