Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ = lim x 5 = 5-5 =0 x5 x lim f x lim 5 x5 x5 lim f x x5 x5 x 5 = lim x 5 x5 = 5-5 = 0 lim f(x) = 0 Hence, lim f x = 0 [When x > 0, x = x] [When x > 0, x = x] Question 28: a bx, x 1 Suppose f(x) = 4, x 1 and if lim f x= f(1) what are possible values of a and b? 1 x b ax x 1 Solution 28: The given function is a bx, x 1 f(x) = 4, x 1 b ax x 1 lim lim f x abx a b x 1 x 1 lim f x limb ax x b a 1 x 1 f(1) = 4 It is given that lim f(x) = f(1). x 1 lim f x lim f x lim f x f 1 x1 x1 x1 a +b = 4 and b – a = 4 On solving these two equations, we obtain a = 0 and b = 4. Thus, the respective possible values of a and b are 0 and 4. 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 29: Let a1, a2,....... n a be fixed real numbers and define a function f(x) = (x - a 1 ) (x - a 2)…..(x - a n ) 1 What is lim f x ? For some a a1, a2,...... a n xa Solution 29: . Compute lim The given function is f(x) = (x - a 1 ) (x - a 2 )…..(x - a n ) lim f x xa 1 = x a x a x a lim 1 2 .... n xa 1 lim lim ... lim n = x a x a x a 1 2 xa1 xa1 xa1 a1 a1 a2 a2 a1 a n ... 0 = lim f(x) = 0 xa 1 Now, lim f(x) = lim xa xa x a1 x a2 ... x an lim 1 lim 2 ... lim n xa xa xa aa aa a a = xa xa xa = 1 2 ... n lim aa aa a a x a f x 1 2 ... n x a f x . Question 30: x 1, x 0 If f(x) = 0, x 0 . x 1 x 1 For what value (s) of does lim f x a xexists? Solution 30: The given function is x 1, x 0 f(x) = 0, x 0 . x 1 x 1 When a = 0, x lim f x lim 1 x0 x0 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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