If [x] denotes the greatest integer less than or equal to $x$, then the value of $\mathop {\lim }\limits_{x \to 1} \left\{ {1 - x + \left[ {x - 1} \right] + \left[ {1 - x} \right]} \right\}$ is

JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

If [x] denotes the greatest integer less than or equal to

x

, then the value of

\lim\limits_{x \to 1} \left\{ {1 - x + \left[ {x - 1} \right] + \left[ {1 - x} \right]} \right\}

View answer and explanation

Correct option: C

- 1

Option C (-1) is correct because both the left-hand limit and the right-hand limit as x approaches 1 are equal to -1, considering the greatest integer function.

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\lim\limits_{h \to 0} 2\left\{ {\frac{{\sqrt 3 \sin \left( {\frac{\pi }{6} + h} \right) - \cos \left( {\frac{\pi }{6} + h} \right)}}{{\sqrt 3 h\left( {\sqrt 3 \cos \,h - \sin \,h} \right)}}} \right\}

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f(x)=\frac{(x+1)^7 \sqrt{1+x^2}}{\left(x^2-x+1\right)^6}

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equals