Ex 12.1, 29
Let a1, a2,….., an be fixed real numbers and define a function
f(x) = (x – a1) (x – a2)…. (x – an)
What is lim┬(x→a"1" ) f(x)? For some a ≠ a1, a2…… an, compute lim┬(x→a) f(x).
f(x) = (x – a1) (x – a2) …….(x – an)
Calculating (𝐥𝐢𝐦)┬(𝐱→𝐚"1" ) f(x)
lim┬(x→a"1" ) f(x) = lim┬(x→a"1" ) (x – a1) (x – a2)….. (x – an)
Putting x = a1
= (a1 – a1) (a1 – a2) …..(a1 – an)
= 0 × (a1 – a2) …… (a1 – an)
= 0
Hence, (𝐥𝐢𝐦)┬(𝐱→𝐚"1" ) f (x) = 0
Calculating (𝐥𝐢𝐦)┬(𝐱→𝐚) f(x)
lim┬(x→a) f(x) = lim┬(x→a) (x – a1) (x – a2) …….(x – an)
Putting x = a
= (a – a1) (a – a2) …… (a – an)
Hence (𝐥𝐢𝐦)┬(𝐱→𝐚) f(x) = (a – a1) (a – a2) ….. (a – an)
Made by
Davneet Singh
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo
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