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anonymous
 5 years ago
find the value of x at which f is not continuous and whether each such value is a removable discontinuity:
(a) f(x) = abs(x) / x
(b) f(x) = (x^2 + 3x) / (x + 3)
(c) f(x) = (x  2) / (abs(x)  2)
anonymous
 5 years ago
find the value of x at which f is not continuous and whether each such value is a removable discontinuity: (a) f(x) = abs(x) / x (b) f(x) = (x^2 + 3x) / (x + 3) (c) f(x) = (x  2) / (abs(x)  2)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0in each of these cases, f will fail to be continuous when the denominator is zero, so for (b), f is discontinuous at x=3. The discontinuity is removable if you can factor things in a way that gets rid of the discontinuity. For example, (b) factors into \[\frac{x(x+3)}{(x+3)} = x\], so the discontinuity is removable.
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