Question

lim x-0 (cosx-(cosx)^2)/(3x^2)

Answer 1

$lim_{x to 0} frac{cosx - cos^{2}x }{3 x^{2} } = [ frac{0}{0} ] = lim_{x to 0} frac{-sinx + 2cosxsinx }{6 x } =[ frac{0}{0} ]=$
$= lim_{x to 0} frac{-sinx- 2sin^{2}x+2cos^{2} x }{6 } = frac{2}{6} = frac{1}{3}$