Limites e sequência numérica, Exercícios de Matemática

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លំហាត់លីមីត

ln 1 (^1) lim x ln 1 2

x x

 x x

2 0

lim ln 2 2

x

x x

x x

x



 

ln 1 arctan (^1) lim x ln 1 arctan 2

x x

 x x

2

3 0

2 ln 1 (^1) lim 2

2 ln 1

x

x x x x

x

x x



0

lim 1 1 1

x

x x

x x



 ^  

0 2

lim x 1 1 2 1 3 1 2

x x x x x px p p

 x x x x px

lim 1 1 1 ln ln 2 3

n n

n

  n n

1 2 3

1 2 1 3 1 4 1 1 lim 1 1 1 1 1

n n

n

n n n n n



 

1

2

lim 1

n n

n

n n n n

n n e



 

2 2 1

1

lim 1!!

n n

n n n

n n

n n e



  

 ^ 

lim 2!

n n

n

n n

  n

2 2 !! lim 2!

n n

n n   n

lim n

n

  n

lim n 7 19 31 12 5

n

  n

6

1

lim 1 n i j k n

ijk

 n    

3 1

4 2

1

lim , 2 1

n^ p n p

n p^ p k

k p k k





  

lim! , 1! 2!!

n

n

p p p n p p n



 

0

lim 1! !

n

n k

n e   k 

  ^  

3 3 (^4 ) 4

1

lim! 1

n

n k

n k k   

2

2

1

lim sin 1

n

n k

k k k   n n n n 

2

1

lim arctan 1 2 1 1 2 1

n

n k

k k k k   n n n n n n 

1 1

sin lim 1 1

n n n n

n

n n n

  n n n

 ^    

(^7 ) 1

sin

lim

n

n k

k

n

k n

  

5

6

1

lim

7 arctan

n

n k

k n

k n k n

  

4 1 (^4 )

5

1

lim 1

k n n

n k

k

n



  

1

0

arctan arctan lim n 1

nx x dx  x

3 5

0 0 3 5

0

lim 1 3 1 2 1

x

x x

x x dx x

x x dx x



1 3 3 1 1

lim ,

1 1

e e

n n n

dx dx n

x x x x

   

  ^ ^

2 2

0

1

sin

1 1 lim 2

x x m

m i n

dx e e mnx x

m m n

  

 

1 (^0 )

lim 1

n n (^) n

dx

x



         

1 2 1 2 2

0

lim 1

n n n n

x x dx



 

4

2

1

lim arctan 1 4

n (^) n

n k

n n k k



  

 ^  

4 2

4 2 1

lim

n

n k

n k k

n k k

  

 ^  