Example 7 - Chapter 12 Class 11 Limits and Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 7 Find the derivative of sin x at x = 0. Let f(x) = sin x We know that fβ(x) = (πππ)β¬(ββ0) πβ‘γ(π₯ + β) β π(π₯)γ/β Here, f(x) = sin x f(x + h) = sin (x + h) Now, fβ(x) = limβ¬(hβ0) π ππβ‘γ(π₯ + β) β π ππ π₯γ/β Putting x = 0 fβ (0) = limβ¬(hβ0) π ππβ‘γ(0 + β) β π ππ (0)γ/β = limβ¬(hβ0) sinβ‘γβ β 0γ/h = limβ¬(hβ0) sinβ‘γβ γ/h = 1 Hence, derivative of sin x at x = 0 is 1 Using limβ¬(xβ0) sinβ‘π₯/π₯ = 1 Replacing x by h limβ¬(xβ0) sinβ‘β/β = 1
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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 and Computer Science at Teachoo