Learn how to solve problems step by step online. Find the limit of (2tan(x)-arcsin(x))/sin(x) as x approaches 0. Rewrite \frac{2\tan\left(x\right)-\arcsin\left(x\right)}{\sin\left(x\right)} in terms of sine and cosine functions. Multiply the single term 2 by each term of the polynomial \left(2\sin\left(x\right)-\arcsin\left(x\right)\cos\left(x\right)\right). If we directly evaluate the limit \lim_{x\to0}\left(\frac{4\sin\left(x\right)-2\arcsin\left(x\right)\cos\left(x\right)}{\sin\left(2x\right)}\right) as x tends to 0, we can see that it gives us an indeterminate form. We can solve this limit by applying L'Hôpital's rule, which consists of calculating the derivative of both the numerator and the denominator separately.

Find the limit of (2tan(x)-arcsin(x))/sin(x) as x approaches 0