dul 1 integer n, -a lim xa x-a he above the ive.

Two integers xa n dy are chosen with replacement out of the set {0,1,,2,3 ,.....10}dot Then find the probability that |x-y|> 5.

Two integers xa n dy are chosen with replacement out of the set {0,1,,2,3 ,.....10}dot Then find the probability that |x-y|> 5.

Two integers xa n dy are chosen with replacement out of the set {0,1,,2,3 ,10}dot Then find the probability that |x-y|> 5.

Two integers xa n dy are chosen with replacement out of the set {0,1,,2,3 ,10}dot Then find the probability that |x-y|> 5.

Evaluate the following limits ([.],~ {.}~ denotes~ greatest integer function and fractional part respectively) (lim)_(x rarr n)[x],(lim)_(x rarr n){x},n in I

Using lim_(xtoa) x=a and the laws of limits prove that lim_(xtoa)x^n =a^n where n is an integer

If [x] denotes the greatest integer less than or equal to x, then evaluate lim_(n rarr oo)(1)/(n^(3)){[1^(2)x]+[2^(2)x]+[3^(2)x]+...}[n^(2)x]}

If [.] denotes the greatest integer function then find the value of lim_(n rarr oo)([x]+[2x]+...+[nx])/(n^(2))

If [x] denotes the greatest integer less than or equal to x, then evaluate lim_(ntooo) (1)/(n^(3))([1^(1)x]+[2^(2)x]+[3^(2)x]+...+[n^(2)x]).

For any positive integer n, lim_(xtoa)(x^(n)-a^(n))/(x-a)=na^(n-1)