Question

lim -(tan)/h=?
h-0

Answer 1

something looks wrong

Answer 2

You mean this?
\[ \lim_{h \rightarrow 0} \frac{\tan h}{h} \]

Answer 3

or this one \[\lim_{h \rightarrow 0}\frac{-\tanh}{h}\]

Answer 4

\[\lim_{h \rightarrow 0}\frac{-\tan h}{h}=\lim_{h \rightarrow 0}\frac{\sin h}{h}\frac{-1}{\cos h}=\lim_{h \rightarrow 0}\frac{\sin h}{h}\lim_{h \rightarrow 0}\frac{-1}{\cos h}=1*(-1)=-1\]

Answer 5

we are using the theorem \[\lim_{h \rightarrow 0}\frac{\sin h}{h}=1\]