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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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Transcript

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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.