Gif Limit!

Calculus Level 3

If lim ⁡ x → a f ( x ) = lim ⁡ x → a ⌊ f ( x ) ⌋ \displaystyle \lim_{x\to a} f(x) = \lim_{x\to a} \lfloor f(x) \rfloor and it exist, then what can we conclude for the value of lim ⁡ x → a f ( x ) \displaystyle \lim_{x\to a} f(x) ?

does not exists. None of These can not be determined. is non-integer. is an integer.

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Nishant Rai by Nishant Rai , 25, India

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1 solution

Marcus Luebke
Jan 31, 2019

The RHS must always be an integer, given that it is the limit of a floor, so the LHS must also be an integer. QED

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