Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ lim f x limnx m x 0 0 m x0 n m Thus, lim f x exists if m = n. lim x0 f x limnx m x 1 1 m x1 n mn 1 3 lim lim f x nx m x1 x1 n 3 m mn lim f x lim f(x) = lim f x x1 x1 Thus, x 1 x 1 lim f x exists for any internal value of m and n. . Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ Exercise 13.2 Question 1: Find the derivative of Solution 1: 2 x - 2 at x = 10. 2 Let f(x) = x â€“ 2. Accordingly, f 10 h f 10 f ' 10 lim h0 h 2 2 10 h 210 2 lim h0 h 2 2 2 10 2.10. h h 210 2 lim h0 h 2 20h h lim h0 h lim 20 h 20 0 20 h0 Thus, the derivative of 2 x â€“ 2 at x = 10 is 20. Question 2: Find the derivative of 99x at x = 100. Solution 2: Let f(x) = 99x. Accordingly, f 100 h f 100 f ' 100 lim h0 h 99100 h99100 lim h0 h 99100 99h 99100 lim h0 h 99h lim h0 h lim 99 99 h0 Thus, the derivative of 99x at x = 100 is 99. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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