Can You Find The Points Of Discontinuity ,if Any A) F(x)=(1/(1-2sinx)) B) F(x)=(3/(5+2cosx))?


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Oddman answered
The points of discontinuity occur where the denominator goes to zero and changes sign.

A) 1-2sin[x] = 0
  1 = 2sin[x]
  1/2 = sin[x].
  This will occur at x=(4n+1)Pi/2±Pi/3 radians = (4n+1)90±60 degrees, where n is any integer.  See the picture.

B) There are no points of discontinuity, because the minimum magnitude the denominator may have is 3. It never goes to zero.

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