" 1."lim_(n rarr oo)n sin((pi)/(4n))cos((pi)/(4n))

Evaluate: (lim_(n rarr oo)n cos((pi)/(4n))sin((pi)/(4n))

lim_(n rarr oo)n sin\ (2 pi)/(3n)*cos\ (2 pi)/(3n)

The value of lim_(n rarr oo)[tan((pi)/(2n))tan((2 pi)/(2n))......tan((n pi)/(2n))]^((1)/(n))

Evaluate lim_(ntooo)ncos((pi)/(4n))sin((pi)/(4n)).

Evaluate lim_(ntooo)ncos((pi)/(4n))sin((pi)/(4n)).

Let f(x) be defined as f(x)=max{a,b,c} where a=lim_(n rarr oo)lim_(alpha rarr1^(+))(alpha^(n)|sin x|+|cos x| alpha^(-n))/(alpha^(n)+alpha^(-n)) , b=lim_(n rarr oo)lim_(alpha rarr1^(-))(alpha^(n)|sin x|+|cos x| alpha^(-n))/(alpha^(n)+alpha^(-n)) , c=lim_(n rarr oo)(pi)/(4n)[1+cos(pi)/(2n)+...+cos((n-1)pi)/(2n)] then The range of f(x) is

lim_(nto oo){n" sin"(2pi)/(3n)."cos"(2pi)/(3n)} =

lim_(n rarr oo)(pi n)^(2/n) =

lim_ (n rarr oo) (1 + sin ((a) / (n))) ^ (n)

If lim_(n rarr oo)(prod_(r=1)^(n)sin((r pi)/(4n))cos((r pi)/(4n)))^((1)/(n))=(a)/(b) a,b in N then find the least value of (a+b)