Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ 1 sin x x h lim h0 h sin x sin x h 1 sin h lim h0 h sin x sin x h sinh 1 lim . lim h0 h h0 sin x .sin x h 1 1 sin x.sin x 0 sin x 2 1. cos ec x .... 2 2 1 lim cos ec x h cos ecx h0 h lim 1 1 1 h0 h sin x h sin x 1 sin x sin x h lim h0 h sin x hsin x 2cos x x h .sin x x h 1 2 2 lim h0 h sin x hsin x 2x h h 2cos sin 1 2 2 lim h0 h sin x hsin x sin h 2x h 2 cos . 2 h 2 lim h0 sin x h sin x 2 cos x h sin h 2 2 lim .lim h0 sin x hsin x h0 h 2 cos x .1 sin xsin x cos ecxcotx ... 3 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 ______________________________________________________________________________ From (1), (2), and (3), we obtain f ' x 3cos ec x 5cos ecx cot x (vi) 2 Let f (x) = 5sin x â€“ 6cos x + 7. Accordingly, from the first principle, f x h f x f ' x lim h0 h 1 lim 5sin x h 6cos x h 7 5sin x 6cos x 7 h0 h 1 lim 5{sin x h sin x} 6{cos x h cos x} h0 h 1 1 5lim [sin x hsin x] 6lim [cos x hcos x] h0h h0h 1 x h x x h x cos xcoshsin xsinhcos x 5lim 2cos sin 6l h0 h 2 2 im h0 h 1 2x h h cos x1cosh sin xsinh 5lim 2cos sin 6lim h0h 2 2 h 0 h h 1 2x h sin 2 cos x1cosh sin xsinh 5lim cos 6lim h0h 2 h h0 h h 2 h 2xh sin 5limcos 2 1cosh sinh h0 2 lim 6 cos x lim sin xlim h 0 0 0 h h h h h 2 2 5cos x.1 6[ cos x . 0 sin x.1] 5cos x6sin x (vii) Let f (x) = 2 tan x â€“ 7 sec x. Accordingly, from the first principle, f x h f x f ' x lim h0 h 1 lim 2tan x h 7sec x h 2tan x 7sec x h0 h 1 lim 2{tan x h tan x} 7{sec x hsec x} h0 h 1 1 2lim [tan x h tan x] 7lim [sec x hsec x] h0h h0h 1 sin x h sin x 1 1 1 2lim 7lim h0h xos x h cos x h0h cos( x h) cos x Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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**Magazine:** CLASS_11_MATHS_SOLUTIONS_NCERT

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