Answer:
2/121
Step-by-step explanation:
Hello,
Hôpital's rule will help here.
[tex]\forall t \in \mathbb{R}^*\\\\f(t)=1-cos(2t)\text{ *** f is differentiable}\\f'(t)=2sin(2t)\\f''(t)=4cost(2t)\\f''(0)=4 \\ \\g(t)=sin^2(11t)\text{ *** g is differentiable}\\g'(t)=2sin(11t)\times 11 \times cos(11t)=2\times 11 sin(11t)cos(11t)\\\\g''(t)=2\times 11 (11cos^2(11t)-11sin^2(11t))\\g''(0)=2\times 11^2[/tex]
So the limit is 4/(2*121)=2/121
Thanks
