Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ = lim x 1 x0 = - 0 + 1 = 1 [If x < 0, x = - x] x lim f x lim 1 x0 x0 = lim x 1 x0 = 0 -1 = - 1 [If x > 0, x = x] Here, it is observed that x 0 x0 lim f x does not exist. When a < 0, x lim f x lim 1 xa xa = lim x 1 xa = - a + 1 lim f x lim f(x). x0 [x < a < 0 x = - x] x lim f x lim 1 xa xa = lim x 1 xa [a < x < 0 x = -x] = - a + 1 lim f x lim f(x) = - a + 1 xa xa Thus, limit of f(x) exists at x = a, where a < 0. When a > 0 lim f x lim x 1 xa xa lim x 1 0 x a x x xa a 1 lim f x lim x 1 xa xa lim x 1 0 a x x x xa a 1 lim f x lim f x a 1 xa xa Thus, limit of f(x)exists at x = a, where a > 0. Thus, lim f x a xexists for all a 0. 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 ______________________________________________________________________________ Question 31: If the function f(x) satisfies Solution 31: f x2 lim x 1 2 x 1 lim f x 2 x1 2 lim x 1 x1 lim x 1 (f(x) – 2) = lim lim 1 lim f(x) – 2) = 0 x1 x (x 2 1 1 2 (f(x) – 2) = x 1 1 lim f(x) - x1 lim 2 = 0 x 1 lim f(x) – 2 = 0 x1 x 1 lim f x 2 f x 2 lim x 1 2 x 1 , evaluate lim f x x 1 . Question 32: 2 mx n x , 0 If f x nx m, 0 x 1. 3 nx m, x 1 For what integers m and n does lim f x x 0 Solution 32: The given function is 2 mx n, x 0 f x nx m, 0 x 1 3 nx m, x 1 0 2 lim lim f x mx n x0 x0 m n 2 n and x 1 lim f x exists? Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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