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Algebraic Identities

x→ nlim -1 [...

Question

$l i m x \to n {(- 1)}^{[x]}$ where [x] stands for greatest integer not exceeding $x$ .

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\infty

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does not exist

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Solution

The correct option is D does not exist
We know $[n + h] = n, [n - h] = n - 1$

$∴ R . H . L . = l i m h \to 0 {(- 1)}^{n} = {(- 1)}^{n}$

$∴ L . H . L . = l i m h \to 0 {(- 1)}^{n - 1} = {(- 1)}^{n - 1} = - {(- 1)}^{n}$

$∴ R . H . L . \neq L . H . L .$
Hence, limit does not exist.
Ans: D

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