Let `f(t)=|[cost,t,1],[2sint,t,2t],[sint,t,t]|` then find `lim_(t->0) f(t)/t^2.`

Let f(t)=|(cost,t,1),(2sint,t,2r),(sint,t,t)| , then {:(lim),(t rarr0):}(f(t))/t^2 is equal to :

Let f(t)=|{:(cos t,,t,,1),(2 sin t,,t,,2t),(sin t,,t,,t):}| .Then find lim_(t to 0) (f(t))/(t^(2))

Let f(t)=|{:(cos t,,t,,1),(2 sin t,,t,,2t),(sin t,,t,,t):}| .Then find lim_(t to 0) (f(t))/(t^(2))

Let f(t)=|{:(cost,t,1),(2sint,t,2t),(sint,t,t):}|" then "underset(trarr0)lim(f(t))/t^2 equal to ".........."

If x=2cost-cos2t,y=2sint-sin2t," then "(dy)/(dx)=

The matrix R(t) is defined by R(t) = [(cost , sin t),(-sint,cost)] . Show that R(s) R(t) = R(s+t).

If =f''(t)cos t+f'(t)sin t,y=-f''(t)sin t+f'(t)cos t, then int[((dx)/(dt))^(2)+((dy)/(dt))^(2)]^((1)/(2))dt is equal to

x=3cost-2cos^(3)t,y=3sint-2sin^(3)t