Learn how to solve addition of numbers problems step by step online. Find the limit of tan(2x)/(x^3) as x approaches 0. If we directly evaluate the limit \lim_{x\to0}\left(\frac{\tan\left(2x\right)}{x^3}\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. After deriving both the numerator and denominator, and simplifying, the limit results in. Apply the property of the quotient of two powers with the same exponent, inversely: \frac{a^m}{b^m}=\left(\frac{a}{b}\right)^m, where m equals 2.

Find the limit of tan(2x)/(x^3) as x approaches 0