Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ 2 1 sin y 4 lim 1 2 1 y0 y 4 Question 18: ax xcos x Evaluate the Given limit: lim x0 bsin x Solution 18: ax xcos x lim x0 bsin x At x = 0, the value of the given function takes the form 0 0 . Now, ax xcos x 1 xacos x lim = lim x0 bsin x b x0 sin x 1 = x lim lim a cos x b x0 sin x x0 1 1 = lima cos x b sin x x0 lim x0 x = 1 b a cos x sin x lim 1 y0 x a1 = b Question 19: Evaluate the Given limit: lim xsec x x0 Solution 19: x 0 0 lim xsec x = lim 0 x0 x0 cos x cos0 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 20: sin ax bx Evaluate the Given limit: lim a, b, a + b ≠ 0 x0 ax sin bx Solution 20: At x = 0, the value of the given function takes the form 0 0 . Now, sin ax bx lim x0 ax sin bx sin ax ax bx ax = lim x0 sin bx ax bx bx sin ax lim lim ax lim bx x 0 ax x 0 x 0 = sin bx limax limbx lim x0 x0 x0 bx x = = = = 1 lim ax limbx sin x 0 x0 lim lim 1 x0 lim ax limbx x0 x x0 x0 lim x0 lim x0 lim (1) x 0 ax bx ax bx Asx 0 ax 0 and bx 0 Question 21: Evaluate the Given limit: lim cosec x cot x x0 Solution 21: At x = 0, the value of the given function takes the form Now, lim cosec x cot x x 0 = lim 1 cos x x0 sin x sin x 1cos x = lim x0 sin x Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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