Multiple choice general knowledge math & puzzles

If the function f(x) = { x^2 - (A + 2) x +A/x-2 for x ¹ 2 is continuous x = 2 then:

  1. A = -1

  2. A = 3

  3. A = 1

  4. A = 0
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For continuity at x=2, evaluate lim(x→2) f(x). Numerator x²-(A+2)x+A = (x-A)(x-1). Limit = (2-A)(2-1)/(2-2) which is undefined unless numerator also zero, requiring A=2 or A=1. Only A=0 makes limit finite: limit = (2-0)/(2-0) = 1, matching f(2). Wait - substituting A=0 gives numerator (x-1)x, limit = 2/2 = 1. Correct.

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