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Question
Sketch the graph of f, then identify the values of x0 for which `lim_(x -> x_0)` f(x) exists.
f(x) = `{{:(x^2",", x ≤ 2),(8 - 2x",", 2 < x < 4),(4",", x ≥ 4):}`
Solution
f(x) = `{{:(x^2",", x ≤ 2),(8 - 2x",", 2 < x < 4),(4",", x ≥ 4):}`
| x | 0 | 1 | 2 | 3 | 3.5 | 4 | 5 | 6 |
| f(x) | x2 | x2 | x2 | 8 – 2x | 8 – 2x | 4 | 4 | 4 |
| f(x) | 0 | 1 | 4 | 2 | 1 | 4 | 4 | 4 |
At x = 4, the curve does not exist.
Hence, except at x0 = 4, the limit of f(x) exists.
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