Question 9 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives

Last updated at April 16, 2024 by

If y = x4 – 10 and if x changes from 2 to 1.99, what is the change in y

(A)0.32   (B) 0.032   (C) 5.68   (D) 5.968

Slide44.JPG

Slide45.JPG

Transcript

Question 9 If y = x4 – 10 and if x changes from 2 to 1.99, what is the change in y 0.32 (B) 0.032 (C) 5.68 (D) 5.968 Since, 𝑥 changes from 2 to 1.99 So, ∆𝒙 = 𝒙_𝟐−𝒙_𝟏 = 1.99 − 2 ∆ 𝑥 = − 0.01 Finding 𝒅𝒚/𝒅𝒙 𝑦=𝑥^4−10 𝑑𝑦/𝑑𝑥 = 4𝒙^𝟑 Putting 𝐱=𝟐, as value of 𝑥 changes from 2 𝑑𝑦/𝑑𝑥= 4(2)^3 𝑑𝑦/𝑑𝑥=𝟑𝟐 Now, ∆𝒚 = 𝒅𝒚/𝒅𝒙 ∆𝒙 Putting values of ∆𝑥 = 0.01 and 𝑑𝑦/𝑑𝑥 = 32 ∆𝑦 = 32 (−0.01) ∆𝒚 = 0.32 ∴ Approximate change in 𝑦 is 0.32 So, the correct answer is (A)

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.