experts please answer--- evaluate lim x tends to 0 tanx - sinx / x3 - Maths - Limits and Derivatives

Question

experts please answer---
evaluate lim x tends to 0 tanx - sinx /
x3

Uday Kiran · Accepted Answer

$n n \underset{n \lim n}{n} n â¢ n n n n \frac{n}{n \tan n â¡ n n x n â¢ n - n n \sin n â¡ n n x n} n n = n \underset{n \lim n}{n} n \frac{n}{n \frac{n}{n \sin n â¡ n n x n} n - n \sin n â¡ n x n} n n = n \underset{n \lim n}{n} n â¢ n n \frac{n}{n \sin n â¡ n n n x n n (n 1 n - n n n \cos n â¡ n n n x n) n n} n n = n \underset{n \lim n}{n} n â¢ n n \frac{n}{n (n 1 n - n n n \cos n â¡ n n n x n) n} n n = n n n \underset{n \lim n}{n} n â¢ n n n n n \frac{n}{n 2 n â¢ n n n n^{n \sin n n n 2 n n} n â¢ n n n \frac{n}{n x n} n} n â¢ n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n (n âˆµ n 1 n â¢ n - n n \cos n â¡ n n 2 n θ n â¢ n = n n 2 n â¢ n n â¢ n n^{n \sin n n n 2 n n} n â¢ n n θ n â¢ n, n n n n \sin n â¡ n 2 n n θ n â¢ n = n n 2 n â¢ n n n n â¢ n \sin n â¡ n â¢ n θ n â¢ n n n n \cos n â¡ n n θ n) n n = n n \underset{n \lim n}{n} n â¢ n n \frac{n}{n 2 n â¢ n n n n^{n \sin n n n 2 n n} n â¢ n \frac{n}{n x n} n} n n = n n n n \frac{n}{n 1 n} n â¢ n n n n ï¿½ n â¢ n n n n \frac{n}{n 1 n} n n = n n n n \frac{n}{n 1 n} n â¢ n n n ï¿½ n â¢ n n n n \frac{n}{n 1 n} n â¢ n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n (n âˆµ n \underset{n \lim n}{n} n â¢ n cos ï¿½ n θ n â¢ n = n n 1 n) n n n = n n n \frac{n}{n 1 n} n n$ hope it helps u thumbs up please