1 Calculate the limit lim r Solutionlimit x infinity x1x2 li

Solution

limit x-> infinity x^(1/x^2)

limit x->infinty 1/x^2 ( x) ^ ( 1/x^2 -1 )

limit x->infinty 1/2x * x^(1/x^2) / x

therefore x tends to infinty,

so limit x-> infinity x^(1/x^2) = infinity

5 a) Given limit n-> infinity a_n exists means take its value as infinity and

limit n-> infinity b_n doesnot exists means take its value as zero(0)

there fore lim n-> infinity (a_n + b_n ) = limit n->infinty a_n + limit n->infinty b_n

  = infinty + 0

= infinity ( exists)

b) given limit n->infinity a_n doesnot exists means zero,

and limit n->infinty b_n doesnot exists means zero

therefore limit n->infinty (a_n + b_n ) = 0 + 0

= 0 (doesnot exists)