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Which of the following functions is not continuous at x = 1?

Practice Questions

Q1
Which of the following functions is not continuous at x = 1?
  1. f(x) = x^2
  2. f(x) = 1/x
  3. f(x) = sin(x)
  4. f(x) = { x, x < 1; 2, x >= 1 }

Questions & Step-by-Step Solutions

Which of the following functions is not continuous at x = 1?
  • Step 1: Understand what continuity means. A function is continuous at a point if you can draw it without lifting your pencil.
  • Step 2: Identify the point we are checking for continuity, which is x = 1.
  • Step 3: Look at the function's behavior around x = 1. Check if the function has any breaks, jumps, or holes at this point.
  • Step 4: If the function has a jump (meaning it suddenly changes value) at x = 1, it is not continuous there.
  • Step 5: Conclude that if there is a jump discontinuity at x = 1, the function is not continuous at that point.
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