Example 7 - Slide 1.jpg

Example 7 - Slide 2.jpg

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  1. Chapter 13 Class 11 Limits and Derivatives
  2. Serial order wise

Transcript

Example 7 Find the derivative of sin x at x = 0. Let f(x) = sin x We know that f’(x) = (π‘™π‘–π‘š)┬(β„Žβ†’0) 𝑓⁑〖(π‘₯ + β„Ž) βˆ’ 𝑓(π‘₯)γ€—/β„Ž Here, f(x) = sin x f(x + h) = sin (x + h) Now, f’(x) = lim┬(hβ†’0) 𝑠𝑖𝑛⁑〖(π‘₯ + β„Ž) βˆ’ 𝑠𝑖𝑛 π‘₯γ€—/β„Ž Putting x = 0 f’ (0) = lim┬(hβ†’0) 𝑠𝑖𝑛⁑〖(0 + β„Ž) βˆ’ 𝑠𝑖𝑛 (0)γ€—/β„Ž = lim┬(hβ†’0) sinβ‘γ€–β„Ž βˆ’ 0γ€—/h = lim┬(hβ†’0) sinβ‘γ€–β„Ž γ€—/h = 1 Hence, derivative of sin x at x = 0 is 1 Using lim┬(xβ†’0) sin⁑π‘₯/π‘₯ = 1 Replacing x by h lim┬(xβ†’0) sinβ‘β„Ž/β„Ž = 1

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