CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
Consider a function f(x) = (x² − 9)/(x − 3). What is the value of lim(x → 3) f(x)?
By factoring x² − 9 as (x − 3)(x + 3) and cancelling the common factor, the limit equals x + 3 evaluated at x = 3, which is 6.
- A0
- B3
- C6Correct
- D9
Explanation
Direct substitution of x = 3 gives 0/0, which is indeterminate. Factor the numerator: f(x) = (x² − 9)/(x − 3) = [(x − 3)(x + 3)]/(x − 3). Cancel (x − 3) to get f(x) = x + 3 for x ≠ 3. Therefore, lim(x → 3) f(x) = 3 + 3 = 6. This limit exists even though f(3) is undefined.
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