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If f(x) = x^2 - 4, what is the limit of f(x) as x approaches 2?

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Question: If f(x) = x^2 - 4, what is the limit of f(x) as x approaches 2?

Options:

  1. 0
  2. 2
  3. 4
  4. Undefined

Correct Answer: 4

Solution: 

The limit as x approaches 2 is f(2) = 2^2 - 4 = 0.

If f(x) = x^2 - 4, what is the limit of f(x) as x approaches 2?

Practice Questions

Q1
If f(x) = x^2 - 4, what is the limit of f(x) as x approaches 2?
  1. 0
  2. 2
  3. 4
  4. Undefined

Questions & Step-by-Step Solutions

If f(x) = x^2 - 4, what is the limit of f(x) as x approaches 2?
  • Step 1: Identify the function f(x) = x^2 - 4.
  • Step 2: Determine the value we are approaching, which is x = 2.
  • Step 3: Substitute x = 2 into the function: f(2) = 2^2 - 4.
  • Step 4: Calculate 2^2, which is 4.
  • Step 5: Subtract 4 from 4: 4 - 4 = 0.
  • Step 6: Conclude that the limit of f(x) as x approaches 2 is 0.
  • Limits – Understanding how a function behaves as it approaches a certain point.
  • Function Evaluation – Calculating the value of a function at a specific point.
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