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Urgent attention required plzzz answer my question fast. .......

Urgent attention required plzzz answer my question fast. .......

Question Image
Grade:11

1 Answers

Aditya Gupta
2075 Points
2 years 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^3
let x=2y
so lim y tends to zero sin^2(y)*tan(y)/8y^3
1/8 coz lim siny/y= lim tany/y= 1
now, s(x)= x/2 – 1/2*sinx
so lim s(x)/x= ½ – ½= 0
also, lim T(x)/s(x)= limsin^2(x/2)*tan(x/2)/(x – sinx)/2
now simply put x=2y and then use l’hospital rule to obtain
lim T(x)/s(x)= 3/2

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