If ${A_i} = \frac{{x - {a_i}}}{{\left| {x - {a_i}} \right|}},\;i = 1,\;2,\; \ldots ,\;n$ and if ${a_1} < {a_2} < {a_3} < \ldots < {a_n}$. Then, $\mathop {\lim }\limits_{x \to {a_m}} \left( {{A_1}{A_2} \ldots {A_n}} \right),\;1 \le m \le n$

Is equal to ${\left( { - 1} \right)^m}$

Is equal to ${\left( { - 1} \right)^{m + 1}}$

Is equal to ${\left( { - 1} \right)^{m - 1}}$

JEE MATHEMATICS MCQ: LIMITS

1 Medium

1 of 1

Analyzing +4 | -1

{A_i} = \frac{{x - {a_i}}}{{\left| {x - {a_i}} \right|}},\;i = 1,\;2,\; \ldots ,\;n

and if

{a_1} < {a_2} < {a_3} < \ldots < {a_n}

. Then,

\lim\limits_{x \to {a_m}} \left( {{A_1}{A_2} \ldots {A_n}} \right),\;1 \le m \le n

View answer and explanation

Correct option: D

Does not exist

Option D (Does not exist) is correct because the left-hand limit and right-hand limit of the product of A_i's as x approaches a_m are not equal, thus the limit does not exist.

JEE MATHEMATICS MCQ: LIMITS

More Questions from LIMITS