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| 1. |
Lim theta tends to 0 ,1-cos theta/ 1-cos3 theta |
| Answer» Let theta=xSo, lim x->0 1-cosx/1-cos3x=lim x->0 2sin^2(x/2) / 2sin^2(3x/2)=[lim x->0 sin(x/2) / sin(3x/2)] [limx->0 sin(x/2) / sin(3x/2)]= [lim x->0 sin(x/2)/(x/2) × lim x->0 (x/2) / sin3x/2)] [ lim x->0 sin(x/2)/(x/2) × lim x->0 (x/2)/sin(3x/2)] = [1× lim 3x/2->0 (3x/2)/sin(3x/2)× lim x->0 (x/2)/(3x/2)] [ 1 × lim 3x/2->0 (3x/2)/sin(3x/2) × lim x->0 (x/2)/(3x/2)]= (1× lim x->0 x/3x)(1×lim x->0 x/3x)= (1/3)(1/3)=1/9, is the required answer. | |