Which of the following is a necessary condition for a function to be continuous at a point?
Practice Questions
1 question
Q1
Which of the following is a necessary condition for a function to be continuous at a point?
The function must be defined at that point
The function must be differentiable at that point
The function must be bounded
The function must be increasing
A function must be defined at a point to be continuous there.
Questions & Step-by-step Solutions
1 item
Q
Q: Which of the following is a necessary condition for a function to be continuous at a point?
Solution: A function must be defined at a point to be continuous there.
Steps: 5
Step 1: Understand what a function is. A function takes an input and gives an output.
Step 2: Know what it means for a function to be continuous. A function is continuous at a point if you can draw it without lifting your pencil.
Step 3: Identify the point where we want to check continuity. Let's call this point 'x'.
Step 4: Realize that for a function to be continuous at point 'x', it must have a value (output) at that point. This means the function must be defined at 'x'.
Step 5: Conclude that if the function is not defined at 'x', we cannot say it is continuous there.
