If Ai-x-ai-x-ai- where i-1-2-3 and a1-a2-a3 then limx- a2A1A2A3-

The correct option is C does not existThe question asks us about,lim x →a^_2 #160; #160; x a^_1|x a^_1|×x a^_2|x a^_2|×x a^_3|x a^_3| Now, since #1 ...

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Byju's Answer

Standard XII

Mathematics

Logarithmic Function

If Ai=x-ai/...

Question

If $A_{i} = \frac{x - a_{i}}{| x - a_{i} |}$ where $i = 1, 2, 3$ and $a_{1} < a_{2} < a_{3}$ then $lim x \to a_{2} A_{1} A_{2} A_{3} =$

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does not exist

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Solution

The correct option is C does not exist
The question asks us about,
lim $x \to a_{2} \frac{x - a_{1}}{| x - a_{1} |} \times \frac{x - a_{2}}{| x - a_{2} |} \times \frac{x - a_{3}}{| x - a_{3} |}$
Now, since
lim $x \to a_{2} \frac{x - a_{2}}{| x - a_{2} |}$ does not exist because
lim $x \to {a_{2}}^{-} \frac{x - a_{2}}{| x - a_{2} |} = - 1$
lim $x \to {a_{2}}^{+} \frac{x - a_{2}}{| x - a_{2} |} = 1$
Since, LHL is not equal to RHL , hence the limit does not exist.
Therefore, the limit of the entire function does not exist

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If Ai=x−ai|x−ai| where i=1,2,3 and a1<a2<a3 then limx→a2A1A2A3=

If $A_{i} = \frac{x - a_{i}}{| x - a_{i} |}$ where $i = 1, 2, 3$ and $a_{1} < a_{2} < a_{3}$ then $lim x \to a_{2} A_{1} A_{2} A_{3} =$