Ex 12.1, 13 - Chapter 12 Class 11 Limits and Derivatives

Last updated at May 7, 2024 by

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Ex 12.1, 13 Evaluate the Given limit: lim┬(x→0) sin⁡〖ax 〗/bx (𝑙𝑖𝑚)┬(𝑥→0) 𝑠𝑖𝑛⁡〖𝑎𝑥 〗/𝑏𝑥 = (𝑙𝑖𝑚)┬(𝑥→0) 𝑠𝑖𝑛 𝑎𝑥" ×" 1/𝑏𝑥 Multiplying & dividing by ax = (𝑙𝑖𝑚)┬(𝑥→0) 𝑠𝑖𝑛 𝑎𝑥" ×" 1/𝑏𝑥 "×" 𝑎𝑥/𝑎𝑥 = (𝑙𝑖𝑚)┬(𝑥→0) 𝑠𝑖𝑛⁡〖𝑎𝑥 〗/𝑎𝑥 "×" 𝑎𝑥/𝑏𝑥 = (𝑙𝑖𝑚)┬(𝑥→0) 𝑠𝑖𝑛⁡〖𝑎𝑥 〗/𝑎𝑥 "×" 𝑎/𝑏 = 𝑎/𝑏 ×(𝒍𝒊𝒎)┬(𝒙→𝟎) 𝒔𝒊𝒏⁡〖𝒂𝒙 〗/𝒂𝒙 Using lim┬(x→0) sin⁡𝑥/𝑥 = 1 Replace x with ax = 𝑎/𝑏 ×𝟏 = 𝒂/𝒃

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