Which of the following is a necessary condition for f(x) to be continuous at x =

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Question: Which of the following is a necessary condition for f(x) to be continuous at x = a?

Options:

Correct Answer: All of the above

Solution:

All conditions must be satisfied for f(x) to be continuous at x = a.

Which of the following is a necessary condition for f(x) to be continuous at x = a?

Which of the following is a necessary condition for f(x) to be continuous at x = a?

Step 1: Understand what it means for a function f(x) to be continuous at a point x = a.
Step 2: Know that for f(x) to be continuous at x = a, three conditions must be met.
Step 3: The first condition is that f(a) must be defined (the function has a value at x = a).
Step 4: The second condition is that the limit of f(x) as x approaches a must exist.
Step 5: The third condition is that the limit of f(x) as x approaches a must equal f(a).
Step 6: If all three conditions are satisfied, then f(x) is continuous at x = a.

No concepts available.