What is limit of: $\displaystyle\lim_{x\to 0}$$\tan x - \sin x\over x$ I want to search limit of this trigonometric function:
$$\displaystyle\lim_{x\to 0}\frac{\tan x - \sin x}{x^n}$$
Note: $n \geq 1$

well to find the limit of [(tan(x)-sin(x))/x]  as x approaches 0 just rewrite tan(x) as a quotient identity i.e tan(x) = sin(x)/cos(x) and divide each term by x separately 
then you will get  sin(x)/(x cos(x))- sin(x)/x now we are free to use difference rule of limits because limit of sin(x)/(x*cos(x)) and sin(x)/x exist and finite i.e both 1.
then limit of [(tan(x)-sin(x))/x]  as x approaches 0 is limit of sin(x)/(x*cos(x)) as x approaches 0 minus limit of sin(x)/x as x approaches 0 which is 1-1=0. thnxs!
