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If f(x) = lim(n->oo) sum(r=0)^n (tan(x/2...

If `f(x) = lim_(n->oo) sum_(r=0)^n (tan(x/2^(r+1)) + tan^3 (x/2^(r+1)))/(1- tan^2 (x/2^(r+1)))` then `lim_(x->0) f(x)/x` is

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The correct Answer is:
1
We have `tanA-tan A/2=(2tanA/2)/(1-tan^(2)A/2)-tanA/2`
`=(tanA/2+tan^(3)A/2)/(1-tan^(2)A/2)`
`f(x)=lim_(nrarroo)sum_(r=0)^(n)(tan x/(2^(r))=tanx/(2^(r+1)))=tanximplieslim_(xrarr0)(f(x))/x=1`
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