Mathematics

Problem

Consider the functions

u(x)=\lfloor x\rfloor

and

v(x)=\operatorname{sgn}(x)

. a. (i) Using their definitions, explain why each function possesses jump discontinuities. b. (ii) Identify all points of discontinuity of

u(x)

and of

v(x)

. Support your answer by evaluating the left-hand and right-hand limits at those points. c. (iii) Compare the magnitude of the jumps at the discontinuities of

u(x)

with that at the discontinuity of

v(x)

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