CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
Consider the function f(x) = (x² - 9)/(x - 3) for x ≠ 3. What is the limit of f(x) as x approaches 3?
The numerator x² - 9 factors as (x - 3)(x + 3). Cancelling (x - 3) from numerator and denominator yields x + 3. As x approaches 3, this simplifies to 3 + 3 = 6.
- A3
- B6Correct
- C9
- D0
Explanation
To find lim(x→3) (x² - 9)/(x - 3), factor the numerator: x² - 9 = (x - 3)(x + 3). Thus f(x) = (x - 3)(x + 3)/(x - 3) = x + 3 for x ≠ 3. As x → 3, the limit is 3 + 3 = 6. A common error is substituting x = 3 directly into the original form, which gives 0/0 (indeterminate), but factoring reveals the true limit.
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