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F(x)=cos(x/x-π) find the point of discontinuity |
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Answer» Answer: Cosine is a continuous function on R. The functions x → x and x → x - π are continuous on R as well. So, for x ≠ π, x/(x - π) is continuous, which implies the composite F(x) = cos(x/(x - π)) is continuous for x ≠ π. At x = π, x → x/(x - π) is not defined and, therefore, neither is f. So, the WAY the function f has been defined, it has no points of discontinuity. It is continuous all over its domain R - {π}. f, however, doesn't have a LIMIT at π. It KEEPS OSCILLATING from -1 to 1 and doesn't approach any value. So, it' not possible to extend f to the reals (defining it at π) in such a way that it is continuous on the whole R. Step-by-step explanation: |
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