Question

How do you find the limit of `(x-tanx)/x^3` as x approaches 0?

Answer 1

In this way:

`lim_(xrarr0)(x-tanx)/x^3=`Hospital`=lim_(xrarr0)(1-1-tan^2x)/(3x^2)=`

`=lim_(xrarr0)-sin^2x/(3x^2cos^2x)=lim_(xrarr0)-(sinx/x)^2*1/(3cos^2x)=`

`=-1^2*1/(3*1)=-1/3`.