Question

find the limits of
lim t->0 sin(cos t)/sec t

Answer 1

\[\lim_{t \rightarrow 0}\sin(\cos(t))/\sec(t)\]\[\sec(t) = 1/\cos(t)\]\[\lim_{t \rightarrow 0}\sin(\cos(t))/(1/\cos(t))=\lim_{t \rightarrow 0}\sin(\cos(t))\cos(t)\]\[\lim_{t \rightarrow 0}\sin(\cos(t))\cos(t)=\sin(\cos(0))\cos(0)=\sin(1)=0\]

Answer 2

\[\sin (1)\]

Answer 3

but we doing special limits

Answer 4

the result is 1/2.. but i dont know how they got that

Answer 5

sorry, it's sin(1) which doesn't = 0 :(, 1/2 doesn't make any sense because as t->0, cos(t) = 1

Answer 6

thats what i did

Answer 7

but the book its making me crazy