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Graphical Method of Solving Linear Programming Problems

The number of...

Question

The number of point(s) of discontinuity of $f (x) = [2 cos x], x \in [0, 2 π]$ ,is (where $[.]$ represents Greatest Integer function)

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Solution

Graph of $2 cos x :$

Graph of $[2 cos x] :$

So, from above graph of $[2 cos x]$
$f (x)$ is discontinuous at ${0, \frac{π}{3}, \frac{π}{2}, \frac{2 π}{3}, \frac{4 π}{3}, \frac{3 π}{2}, \frac{5 π}{3}, 2 π}$
So, there are $8$ points of discontinuity.

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Graphical Method of Solving Linear Programming Problems

Standard XII Mathematics

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