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11%20-%20Limit - PROBLEMS 11 LIMIT Page 1 Find the...

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PROBLEMS 11 - LIMIT Page 1 Find the following limits : ( 1 ) 3 5x 5 3x 5 3x 7 x lim 1 x + + + + - - [ Ans: 1 ] ( 2 ) 1 x 1 x 1 x lim 4 3 2 1 x - - - + + [ Ans: 2 ( 2 - 3 ) ( 3 ) dx sin cx sin bx sin ax sin lim 0 x - - d c b a : Ans - - ( 4 ) x 4 tan x 1 lim x 4 π π - - [ Ans: 2 ] ( 5 ) x 4 sin x cos x lim x 4 π π - - [ Ans: - 2 ] ( 6 ) x 4 sin 3x cos 3x lim x 4 + π π - [ Ans: - 3 2 ] ( 7 ) 1 x 3 tan x 3 lim x 3 π - - - 4 1 : Ans ( 8 ) x 6 2 sin x 1 lim 3 tan x 1 π - - 4 3 : Ans ( 9 ) 1 x 1 x 1 x lim 7 5 3 1 x + + + + + - 1 Ans: ( 35 21 ) 7 + ( 10 ) 1 x n x ..... x x x lim n 3 2 1 x - - + + + + + 2 ) 1 n ( n : Ans ( 11 ) 9 15x 2x 6 x 8x x lim 3 2 4 3 x - - - - - 39 59 : Ans ( 12 ) 3 1 3 1 6 2 x 2 x 64 x lim - - × 2 9 : Ans 3 20 ( 13 ) 8 x ) 1 4x ( ) 3 3x ( lim 3 4 1 4 1 2 x - - + + 3 144 1 : Ans - ( 14 ) 4 x 4 2x 6 x lim 2 3 3 2 x - - + + 48 1 : Ans -
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PROBLEMS 11 - LIMIT Page 2 Find the following limits : 1 1 x 2 sin x 6 ( 15 ) lim 2x 1 π - - - 3 1 : Ans ( 16 ) a tan x tan a tan x tan lim 1 1 a x - - - - [ ] a sec ) a 1 ( : Ans 2 2 + ( 17 ) dx cos cx cos bx cos ax cos lim 0 x - - d c b a : Ans 2 2 2 2 - - ( 18 ) 2 1 n n n a x ) a x ( ) a x ( na ) a x ( lim - - - - - a 2 ) 1 n ( n : Ans 2 n - - ( 19 ) 2 m n 0 x x ) nx 1 ( ) mx 1 ( lim + + - 2 ) m n ( mn : Ans - ( 20 ) x 1 n x 1 m lim n m 1 x - - - , m, n N 2 n m : Ans - ( 21 ) N n , ) 1 x ( n x ) 1 n ( x lim 2 1 n 1 x + + + - - + 2 ) 1 n ( n : Ans ( 22 ) [ ] 2 2 2 2 n 1 3 5 ... ( 2n 1 ) lim 1 3 5 ... ( 2n 1 ) n → ∞ + + + + + + + + - - 3 4 : Ans ( 23 ) x sin 2 2 lim 3x 5x 0 x - [ ] 2 log 2 : Ans ( 24 ) x 1 0 x x 1 x 1 lim + - 2 Ans: e - ( 25 ) e x 1 x log lim e x - - [ ] e : Ans 1 - ( 26 ) n r n 1 r n 3 n 1 lim = e log 2 : Ans 3 ( 27 ) + ) 1 n ( n 1 lim x , n N [ Ans: 1 ] ( 28 ) 2 3 x n n n lim , n N 4 3 : Ans ( 29 ) + + n 1 n n lim 2 n - 2 1 : Ans ( 30 ) x x 0 x e 2 e x tan x lim - - + [ Ans: 1 ]
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PROBLEMS 11 - LIMIT Page 3 Find the following limits : ( 31 ) x 2 2e e lim x 2x 3x 0 x + - e 2 log : Ans ( 32 ) 2 x x x 0 x x 1 2 3 6 lim + - - [ ] ) 2 log ( ) 3 log ( : Ans ( 33 ) 2 2 4 4 0 x x 1 x 1 x lim + + - 2 1 : Ans - ( 34 ) 1 x x 3 x 7 lim
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