Solve: \(lim ((sin^2x-x^2) / (x^4))\)
x→0
given that:
\(lim ((x-sinx)/(x^3)) = 1/6\)
See this:
https://www.symbolab.com/solver/limit-calculator/%5Clim_%7Bx%5Cto0%7D%5Cleft(%5Cfrac%7B%5Cleft(sin%5E%7B2%20%7Dx%20%20-%20x%5E%7B2%7D%5Cright)%7D%7Bx%5E%7B4%7D%7D%5Cright)
(sin^2 x - x^2) / x^4 =
- ( x^2 - sin ^2x) / x^4 =
- ( x -sin x) / x^3 * ( x + sin x ) / x
- ( 1/6) ( x /x + sinx/x) =
-(1/6) ( sin x / x + x/x ) =
as x → 0 sin x / x = 1 and x /x =1
-(1/5) ( 1 + 1) =
-(1/6) (2) =
-2/6 =
-1/3
+4 
