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Examine the continuity of f(x)=x2-9x -3, for x≠3=8, for x=3} at x = 3 - Mathematics and Statistics

Sum

Examine the continuity of `"f"(x) = {:((x^2 - 9)/(x  - 3)",",  "for"  x ≠ 3),(=8",",  "for"  x = 3):}}` at x = 3

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Solution

f(3) = 8     ...(Given)  ...(1)

`lim_(x -> 3) "f"(x) =  lim_(x -> 3) (x^2 - 9)/(x - 3)`

= `lim_(x -> 3) ((x - 3)(x + 3))/(x - 3)`

= `lim_(x -> 3) (x + 3)`   ...[∵ x → 3, x ≠ 3, ∴ x – 3 ≠ 0]

= 3 + 3

= 6    ...(2)

From (1) and (2),

f(3) ≠ `lim_(x -> 3) "f"(x)`

∴ f is discontinuous at x = 3.

  Is there an error in this question or solution?
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