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Question:

For each x ∈ R, let [x] be the greatest integer less than or equal to x. Then limx→0⁻ -x([x] + |x|)sin([x])/|x| is equal to

sin1

0

1

-sin1

Solution:

The correct option is A -sin1
limx→0⁻ -x([x] + |x|)sin([x])/|x|
When x→0⁻, [x] = -1, |x| = -x ⇒ limx→0⁻ -x(-1 - x)sin(-1)/-x = -sin1