NCERT Class XI Mathematics - Limits and Derivatives - Solutions

Question : 29

Total: 72

Let a1,a2 ,........., an be fixed real numbers and define a functionf(x) = (x – a1) (x – a2) ......... (x – an). What is

lim

x→a1

f (x) ? For some a ≠ a1,a2 , ... , an compute

lim

x→a

f (x).

Solution:

We have, f(x) = (x – a1) (x – a2) ......... (x – an)
∴

lim

x→a1

f (x) = f (a1)
= (a−a1)(a1−a2) ... (a1−an)
∴

lim

x→a1

f (x) = 0
We have f(x) = (x−a1)(x−a2) ... (x−an)
∴

lim

x→a

f (x) = (a−a1)(a−a2) ... (a−an)

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