What is lim x→2 (x² - 4)/(x - 2)?
Answer and explanation
Correct answer: 4
Direct substitution gives 0/0, so factor the numerator: x² - 4 = (x - 2)(x + 2). For x ≠ 2, the expression simplifies to x + 2. Therefore, as x approaches 2, the limit is 2 + 2 = 4. Option 2 is only the approaching value of x, not the value of the limit. Exam tip: when direct substitution gives 0/0, factorise and cancel the common factor first.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Direct substitution gives 0/0, so factor the numerator: x² - 4 = (x - 2)(x + 2). For x ≠ 2, the expression simplifies to x + 2. Therefore, as x approaches 2, the limit is 2 + 2 = 4. Option 2 is only the approaching value of x, not the value of the limit. Exam tip: when direct substitution gives 0/0, factorise and cancel the common factor first.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Limits and Derivatives. Topic: Limits of polynomials and rational functions.
