Find the number of discontinuities of the given function between x = 0 and x =2.

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Solution

On the graph we see 3 points of discontinuities between points 0 and 2. One discontinuity is of removable type (a) and 2 jump discontinuities of non removable type. (b, c).

We get jump discontinuities when the left hand and right hand limits are not equal. There is an obvious jump in the curve. In case of removable discontinuity a finite limit exists but the value of the function will be different from this limit.

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Find the number of discontinuities of the given function between x = 0 and x =2.

f (x) = \frac{1}{x + 2}

f (x) = \frac{1}{x - 1} .

f [f {f (x)}] .

f (x) = [6 sin x], 0 \leq x \leq π

[.]

f (x) = {\begin{matrix} [cos π x], & 0 \leq x \leq 1 | x - 1 | [x - 2], & 1 < x \leq 2 \end{matrix}

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