Posted by claire on .
Limit as x approaches zero of (sinx-(x^3/6)/x^5)
math please help -
I assume you forgot the parentheses in the numerator,
Lim (sin(x)-(x^3/6))/x^5 as x->0
It would be easy to change sin(x) to a polynomial, the limits of which are easy to find.
If you expand sin(x) by Taylor's series, you'd get
So the expression becomes
(x-2x³/6+x^5/120-x^7/5040+...)/x^5 as x->0
which gives +∞
However, if the question had been
Lim (sin(x)-(x-x³/6))/x^5, the result would be 1/120