Learn how to solve differential calculus problems step by step online. Find the limit of (x+sin(2x))/(sin(x)cos(x)) as x approaches 0. Simplify \sin\left(x\right)\cos\left(x\right) using the trigonometric identity: \sin(2x)=2\sin(x)\cos(x). Divide fractions \frac{x+\sin\left(2x\right)}{\frac{\sin\left(2x\right)}{2}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Multiply the single term 2 by each term of the polynomial \left(x+\sin\left(2x\right)\right). If we directly evaluate the limit \lim_{x\to0}\left(\frac{2x+2\sin\left(2x\right)}{\sin\left(2x\right)}\right) as x tends to 0, we can see that it gives us an indeterminate form.

Find the limit of (x+sin(2x))/(sin(x)cos(x)) as x approaches 0