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one year ago

```							by applying usual geometric formula we will see that T(x)= sin^2(x/2)*tan(x/2)so lim x tends to zero T(x)/x^3= lim x tends to zero sin^2(x/2)*tan(x/2)/x^3let x=2yso lim y tends to zero sin^2(y)*tan(y)/8y^3= 1/8 coz lim siny/y= lim tany/y= 1now, s(x)= x/2 – 1/2*sinxso lim s(x)/x= ½ – ½= 0also, lim T(x)/s(x)= limsin^2(x/2)*tan(x/2)/(x – sinx)/2now simply put x=2y and then use l’hospital rule to obtainlim T(x)/s(x)= 3/2
```
one year ago
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