Solution. The correct option is C There are exactly two possible values of n. f(x) =sgn(sin2x−sinx−1) is discontinuous when sin2x−sinx−1= 0 ⇒ sinx = 1+√5 2 or sinx= 1−√5 2 ⇒ sinx = 1−√5 2 (∵sinx ∈[−1,1]) Dotted line represents y= 1−√5 2. For exactly four points of discontinuity, n can take value 4 or 5 as shown ...
This information is part of the Modelica Standard Library maintained by the Modelica Association. This function approximates sqrt (abs (x))*sgn (x), such that the derivative is finite and smooth in x=0. With the default value of delta=0.01, the difference between sqrt (x) and regRoot (x) is 16% around x=0.01, 0.25% around x=0.1 and 0.0025% ...
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