Formal Definition of Limits: In Problems

61-72,\\\\lim_(n->\\\\infty )a_(n)=a

Find the limit

a

, and determine

N

so that

|a_(n)-a|

for all

n>N

for the given value of

\\\\epsi lon

.\ 61.

a_(n)=(1)/(n),\\\\epsi lon=0.01

\ 62.

a_(n)=(1)/(n),\\\\epsi lon=0.02

\ 63.

a_(n)=(1)/(n^(2)),\\\\epsi lon=0.01

\ 64.

a_(n)=(1)/(n^(2)),\\\\epsi lon=0.001

\ 65.

a_(n)=(1)/(\\\\sqrt(n)),\\\\epsi lon=0.1

\ 66.

a_(n)=(1)/(\\\\sqrt(n)),\\\\epsi lon=0.05

\ 67.

a_(n)=((-1)^(n))/(n),\\\\epsi lon=0.01

\ 68.

a_(n)=e^(-n),\\\\epsi lon=0.01

Formal Definition of Limits: In Problems 61-72, limnan=a Find the limit a, and determine N so that anaN for the given value of . 61. an=n1,=0.01 62. an=n1,=0.02 63. an=n21,=0.01 64. an=n21,=0.001 65. an=n1,=0.1 66. an=n1,=0.05 67. an=n(1)n,=0.01 68. an=en,=0.01