If , where denotes the greatest integer function,…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

If f(x)={sin⁡πx2,x<1[x],x≥1f(x) = \begin{cases} \sin \frac{\pi x}{2}, & x < 1 \\ [x], & x \ge 1 \end{cases}, where [x][x] denotes the greatest integer function, then (1) f(x)f(x) is continuous at x=1x=1 (2) f(x)f(x) is discontinuous at x=1x=1 (3) f(1+)=0f(1^+) = 0 (4) f(1−)=−1f(1^-) = -1

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