For `n in N,` let `f_(n) (x) = tan ""(x)/(2) (1+ sec x ) (1+ sec 2x) (1+ sec 4x)……(1+ sec 2 ^(n)x),` the `lim _(xto0) (f _(n)(x))/(2x)` is equal to :

What is lim_(xto0) ((1+x)^(n)-1)/(x) equal to ?

lim_(xto0) ((2^(m)+x)^(1//m)-(2^(n)+x)^(1//n))/(x) is equal to

lim_ (n rarr oo) (1) / (2) tan ((x) / (2)) + (1) / (2 ^ (2)) tan ((x) / (2 ^ (2))). ... + (1) / (2 ^ (n)) tan ((x) / (2 ^ (n))) is equal to lim_ (n rarr oo) sum_ (n = 1) ^ (n) (1 ) / (2 ^ (n)) tan ((x) / (2 ^ (n)))