lim-x-cos-pi-2-sin-3-x-x-sin-3-x-2-1-x-

Question Number 177570 by mathlove last updated on 07/Oct/22

\lim_{Δ x \to c o s \frac{π}{2}} \frac{{s i n}^{3} (Δ x + x) - {s i n}^{3} x}{2^{- 1} Δ x} = ?

Commented by blackmamba last updated on 07/Oct/22

\cos \frac{π}{2} = 0 ?

Commented by blackmamba last updated on 07/Oct/22

\lim_{Δ x \to 0} \frac{\sin^{3} (x + Δ x) - \sin^{3} x}{\frac{1}{2} Δ x} ?

Commented by mathlove last updated on 07/Oct/22

Δ x \to c o s \frac{π}{2}

Commented by mathlove last updated on 07/Oct/22

y e s

Commented by mathlove last updated on 07/Oct/22

a n y o n e s o l v e t h i s q u s t i o n

Answered by mr W last updated on 07/Oct/22

\lim_{Δ x \to c o s \frac{π}{2}} \frac{{s i n}^{3} (Δ x + x) - {s i n}^{3} x}{2^{- 1} Δ x}

= 2 \lim_{Δ x \to 0} \frac{{s i n}^{3} (Δ x + x) - {s i n}^{3} x}{Δ x}

= 2 \times {(\sin^{3} x)}^{'}

= 6 \sin^{2} x \cos x

Commented by mathlove last updated on 08/Oct/22

t h a n k s a l o t s i r