Question:
lim x approch to 0 x³cotx÷1- cosx
Answer:
Given limx->0 {(x3 * cotx)/(1-cosx)}
= limx->0 [(x3 * cosx)/{(sinx*(1-cosx)}
= limx->0 [(x3 * cosx)/{sinx*2sin2 (x/2)}]
= limx->0 [{x*(x2 /4) * 4* cosx)}/{sinx*2*sin2 (x/2)}]
= {limx->0 (x2 /4)/sin2 (x/2)} * {limx->0 x/sinx}*{limx->0 cosx} *(4/2) {since limx->0 x/sinx = 1, limx->0 cosx = 1}
= 2
So value of limx->0 {(x3 * cotx)/(1-cosx)} = 2
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