Question

lim x-> 0+ sin^-1 2x / x help please

Answer 1

Are you asking
\[\lim_{x\to 0^+}\frac{\sin^{-1} (2x)}{x}\]

Answer 2

\(\Large\color{black}{\displaystyle\lim_{x \rightarrow ~0^+}~\frac{\sin^{-1}(2x)}{x}}\)

~ \(\Large\color{black}{\sin^{-1}(0)=0}\)

sounds like it is an L'H'S problem.

Answer 3

or plug in x = (sin y)/2
:)

Answer 4

when x->0+
y->0+

Answer 5

Let \(f(x)=\sin^{-1}(2x)\). Then the limit that you are looking for is the definition of \(f'(0)\).