Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ Question 10: Evaluate the Given limit: Solution 10: z lim z1 z 1 3 1 6 1 1 z lim z1 z 1 3 1 6 1 1 At z = 1, the value of the given function takes the form 0 0 . Put 1 6 z = x so that z Ã¢â€ ’1 as x Ã¢â€ ’ 1. Accordingly, x 2 1 lim x1 x 1 z lim z1 z 1 3 1 6 1 = 1 x 2 1 lim x1 x 1 x a 2.1 lim xa xa 2 z lim z1 z n n 21 n1 1 3 1 6 1 = 2 1 na Question **11**: Evaluate the Given limit: Solution **11**: 2 = 1 1 2 1 1 2 ax bx c lim x 1 2 cx bx a 2 ax bx c 2 lim x1 cx b a , a + b + c 0 a b c c b a = a b c abc = 1 [a + b + c 0] 1 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 12: Evaluate the Given limit: Solution 12: 1 1 lim x 2 x2 x 2 1 1 lim x 2 x 2 x2 At x = â€“2, the value of the given function takes the form 0 0 1 1 Now, lim x 2 x2 x 2 = lim 1 x2 2 x 1 1 2 2 4 = 2 x 2x lim x 2 x2 Question 13: sin ax Evaluate the Given limit: lim x 0 bx Solution 13: sin ax lim x 0 bx At x = 0, the value of the given function takes the form 0 0 . sin ax sin ax ax Now, lim = lim x 0 bx x 0 ax bx sin ax a lim x 0 ax b a sin ax lim x 0 ax 0 b ax0 ax a sin y 1 lim 1 b y0 y a b Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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