Title 11.LIMITS AND DERIVATIVES.pdf ✅

11. LIMITS AND DERIVATIVES-MCQS TYPE (1.) Let f R R : → be a positive increasing function with ( ) ( ) 3 lim 1 x f x f x → = . Then ( ) ( ) 2 limx f x f x → = [AIEEE-2010] (a.) 1 (b.) 2 3 (c.) 3 2 (d.) 3 (2.) Let f R: 0, →  ) be such that limx→5 f x( ) exists and ( ) 2 5 ( ) 9 lim 0 5 x f x x → − = − . Then limx→5 f x( ) equals [AIEEE-2011] (a.) 2 (b.) 3 (c.) 0 (d.) 1 (3.) ( )( ) 0 1 cos2 3 cos lim tan4 x x x x x → − + is equal to [JEE (Main)-2013] (a.) 1 4 − (b.) 1 2 (c.) 1 (d.) 2 (4.) ( ) 2 2 0 sin cos lim x x x  → is equal to[JEE (Main)-2014] (a) − (b)  (c) 2  (d) 1 (5.) ( )( ) 0 1 cos2 3 cos lim tan4 x x x x x → − + is equal to [JEE (Main)-2015] (a.) 4 (b.) 3 (c.) 2 (d.) 1 2 (6.) Let ( ) 1 2 2 0 lim 1 tan x x p x = + → + then logp is equal to [JEE (Main)-2016] (a.) 1 (b.) 1 2 (c.) 1 4 (d.) 2 (7.) ( )( ) 1/ 2 1 2 3 lim n n n n n n n →   + +      is equal to [JEE (Main)-2016] (a.) 2 27 e (b.) 2 9 e (c.) 3log3 2 − (d.) 4 18 e