Question

lim de x->0 tan2x/x

Answer 1

@karen95 Hi,

\(\huge \color{red}{\text{Welcome to Open Study}}\ddot\smile\)

just to clarify, is it \(\tan^2x \: \: or \: \: \tan 2x\) ??

Answer 2

\[\lim x \rightarrow 0 \frac{ \tan2x }{ x }\] hola tu podrias ayudarme sobreeltema

Answer 3

so, write , tan2x = sin2x/cos 2x first.
and use \(\lim \limits{x \rightarrow 0} \:\: \sin x/x=1\)

also, can i request you to reply in english, so that i don't have to use google translate everytime ?:P

Answer 4

\[\lim_{x\to0}\frac{\tan(2x)}{x}=\lim_{x\to0}\frac{\sin(2x)}{x\cos(2x)}=\lim_{x\to0}\frac{\sin(2x)}{x}\cdot\lim_{x\to0}\frac{1}{\cos(2x)}\]
I haven't used Spanish in a while, but here goes: Para il primero limite, multiplica la fraccion por \(\frac{2}{2}\):
\[\frac{2}{2}\cdot\lim_{x\to0}\frac{\sin(2x)}{x}\cdot\lim_{x\to0}\frac{1}{\cos(2x)}\\
2\lim_{x\to0}\frac{\sin(2x)}{2x}\cdot\lim_{x\to0}\frac{1}{\cos(2x)}\]
Ahora, usa el dato che
\[\lim_{x\to0}\frac{\sin(ax)}{ax}=1\]
por valores de \(a>0.\)