lim_(n rarr oo){(1)/(2)tan(x)/(2)+(1)/(2^(2))tan(x)/(2^(2))+(1)/(2^(3))tan(x)/(2^(3))+.........+(1)/(2^(n))tan(x)/(2)

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)))

lim_ (n rarr oo) (1) / (2) tan ((x) / (2)) + (1) / (2 ^ (2)) tan ((x) / (2 ^ (2))). .. + (1) / (2 ^ (n)) tan ((x) / (2 ^ (n)))

(1)/(2) tan"" ((x)/(2) ) + (1)/( 4) (tan"" (x)/(4) ) + ...... + (1)/(2^(n) ) tan"" ((x)/( 2^n) ) =

If cos ((x) / (2)) cos ((x) / (2 ^ (2))) cos ((x) / (2 ^ (3))) ...... oo = (sin x ) / (x) (1) / (2) tan ((x) / (2)) + (1) / (2 ^ (2)) tan ((x) / (2 ^ (2))) + ( 1) / (2 ^ (3)) tan ((x) / (2 ^ (3))) ... oo

lim_(x rarr oo)tan^(-1)(x^(2)-x^(4))

lim_(x rarr0)x((tan^(-1)((x+1)/(x+2))-tan^(-1)((x)/(x+2)))=

lim_(x rarr0)(tan^(2)x-x^(2))/(x^(2)tan^(2)x)

If f(x)=lim_(n rarr oo)(tan pi x^(2)+(x+1)^(n)sin x)/(x^(2)+(x+1)^(n)) then