Example 7 - Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)
Last updated at Nov. 30, 2019 by Teachoo
Examples (Term 1 and Term 2)
Example 1 (i)
Example 1 (ii)
Example 1 (iii)
Example 2 (i)
Example 2 (ii) Important
Example 2 (iii) Important
Example 2 (iv)
Example 2 (v)
Example 3 (i) Important
Example 3 (ii) Important
Example 4 (i)
Example 4 (ii) Important
Example 5
Example 6
Example 7 Important You are here
Example 8
Example 9
Example 10 Important
Example 11
Example 12
Example 13 Important
Example 14
Example 15 Important
Example 16
Example 17 Important
Example 18
Example 19 (i) Important
Example 19 (ii)
Example 20 (i)
Example 20 (ii) Important
Example 21 (i)
Example 21 (ii) Important
Example 22 (i)
Example 22 (ii) Important
Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)
Serial order wise
- Ex 13.1 (Term 1)
- Ex 13.2 (Term 2)
-
Examples (Term 1 and Term 2)
- Miscellaneous (Term 1 and Term 2)
Transcript
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
