 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/discrete-mathematics-continuous-mathematics-and-probability-resit/6/a/iii/solution

The left and right limits at zero are

- 1

and

1

\frac{f ( 0 ^{-} ) + f ( 0 ^{+} )}{2} = \frac{- 1 + 1}{2} = 0.

Indeed every term

sin ((2 j + 1) π x)

is zero at

x = 0

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