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Ex 13.1, 25 - Find lim x -> 0 where f(x) = { |x| / x, 0 - Teachoo

Ex 13.1, 25 - Chapter 13 Class 11 Limits and Derivatives - Part 2

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Ex 13.1, 25 Evaluate lim┬(x→0) f(x), where f(x) = {█(|x|/x@0,)┤, ■8(x≠0@x=0) Finding limit at x = 0 LHL at x → 0 lim┬(x→0^− ) f(x) = lim┬(h→0) f(0 − h) = lim┬(h→0) f(−h) = lim┬(h→0) (|−ℎ|)/(−ℎ) = lim┬(h→0) ℎ/(−ℎ) = lim┬(h→0) −1 = −1 RHL at x → 0 lim┬(x→0^+ ) f(x) = lim┬(h→0) f(0 + h) = lim┬(h→0) f(h) = lim┬(h→0) (|ℎ|)/ℎ = lim┬(h→0) ℎ/ℎ = lim┬(h→0) 1 = 1 Since LHL ≠ RHL ∴ (𝒍𝒊𝒎)┬(𝒙→𝟎) f(x) doesn’t exist

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.