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

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

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  1. Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)
  2. Concept wise

Transcript

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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.