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Q34Section B (Section B)34 of 60

Continuity at a point for functions involving a floor term

For x∈Rx\in\mathbb R, define f(x)=cos⁡(πx)+[x2]f(x)=\cos(\pi x)+\left[x^2\right] and g(x)=sin⁡(πx)g(x)=\sin(\pi x). Which of the following statements is (are) TRUE?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Options

Select every correct option, then submit.