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Example 22 - Use differential to approximate (25)1/3 - Examples

Example 22 - Chapter 6 Class 12 Application of Derivatives - Part 2
Example 22 - Chapter 6 Class 12 Application of Derivatives - Part 3

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Example 22 Use differential to approximate γ€–(25)γ€—^(1/3)Let 𝑦 =π‘₯^(1/3) Where π‘₯=27 and β–³π‘₯=βˆ’2 Since π’š =𝒙^(𝟏/πŸ‘) 𝑑𝑦/𝑑π‘₯=𝑑(π‘₯^(1/3) )/𝑑π‘₯ = 1/3 π‘₯^(1/3 βˆ’ 1) = 1/3 π‘₯^((βˆ’2)/3) 𝑑𝑦/𝑑π‘₯=1/(3π‘₯^(2/3) ) Now, βˆ†π’š=π’…π’š/𝒅𝒙 βˆ†π’™ βˆ†π‘¦= 1/(3π‘₯^(2/3) ) βˆ†π‘₯ Putting values βˆ†π‘¦= 1/(3(27)^(2/3) ) (βˆ’2) βˆ†π‘¦= (βˆ’2)/(3 Γ—(3^3 )^(2/3) ) βˆ†π‘¦= (βˆ’2)/(3 Γ— 3^2 ) βˆ†π‘¦= (βˆ’2)/27 βˆ†π’š=βˆ’πŸŽ.πŸŽπŸ•πŸ’ Now, (πŸπŸ“)^(𝟏/πŸ‘) =π’š+βˆ†π’š Putting values (25)^(1/3)=(27)^(1/3)βˆ’0.074 (25)^(1/3)=(3^3 )^(1/3)βˆ’0.074 (25)^(1/3)=3βˆ’0.074 (πŸπŸ“)^(𝟏/πŸ‘)=𝟐.πŸ—πŸπŸ” Hence, approximate value of (25)^(1/3) is 𝟐.πŸ—πŸπŸ”

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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.