Evaluate `lim_(xto0) {(sinx-x+(x^(3))/(6))/(x^(5))}.`

Answer

`1//120`

Explanation

`underset(xto0)lim(sinx-x+(x^(3))/(6))/(x^(5))=underset(xto0)lim(x-(x^(3))/(3!)+(x^(5))/(5!)-(x^(7))/(7!)+* * *-x+(x^(3))/(6))/(x^(5))`
`=underset(xto0)lim((1)/(5!)-(x^(2))/(7!)+...)=(1)/(120)`