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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 29 of 72
Marks: +1, -0
Let a1,a2a_1, a_2 ,........., ana_n be fixed real numbers and define a functionf(x) = (x – a1a_1) (x – a2a_2) ......... (x – ana_n). What is lim⁡x→a1\lim\limits_{x\rightarrow a_1} f (x) ? For some a ≠ a1,a2a_1, a_2 , ... , ana_n compute lim⁡x→a\lim\limits_{x\rightarrow a} f (x).
Solution:  
We have, f(x) = (x – a1a_1) (x – a2a_2) ......... (x – ana_n)
∴ lim⁡x→a1\lim\limits_{x\rightarrow a_1} f (x) = f (a1)(a_1)
= (a−a1)(a1−a2)(a-a_1)(a_1-a_2) ... (a1−an)(a_1-a_n)
∴ lim⁡x→a1\lim\limits_{x\rightarrow a_1} f (x) = 0
We have f(x) = (x−a1)(x−a2)(x-a_1)(x-a_2) ... (x−an)(x-a_n)
∴ lim⁡x→a\lim\limits_{x\rightarrow a} f (x) = (a−a1)(a−a2)(a-a_1)(a-a_2) ... (a−an)(a-a_n)
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