" (vi) "lim_(theta rarr0)(tan3 theta-sin3 theta)/(theta^(3))

lim_(theta rarr 0)(tan theta - sin theta)/(theta^(3))=

lim_(theta rarr0)(3tan theta-tan3 theta)/(2 theta^(3))

lim_(theta rarr 0)(sin 5 theta - sin 3 theta)/(theta)=

lim_(theta rarr0)cot theta-csc theta

Using L'Hospital 's rule prove that lim_(theta rarr 0) (theta-sintheta)/(theta^3)=1/6

lim_(x rarr0)(sin^(3)theta*tan^(3)theta)/(theta^(6))

Let l=lim_(theta rarr0)(sin^(3)theta -tan^(3)theta)/(theta^(5)) and m=lim_(theta rarr(pi)/(4))(((sin theta+cos theta)^(3)-2sqrt(2))/(1-sin2 theta)) .Find the value of [l^(2)+m^(2)] (where [x] denotes largest integer less than or equal to

lim_(theta rarr0)((sin theta)/(sin((theta)/(2))))=2

lim_(theta rarr 0) (cos5 theta - cos 7 theta )/(theta^(2)) =