f-a-is-derivative-of-function-f-a-lim-h-0-f-a-2h-2-f-a-h-3-h-2-

Question Number 161516 by naka3546 last updated on 19/Dec/21

f^{'} (a) i s d e r i v a t i v e o f f u n c t i o n f (a) .

\lim_{h \to 0} \frac{f (a - 2 h^{2}) - f (a + h^{3})}{h^{2}} = ?

Commented by cortano last updated on 19/Dec/21

= \lim_{h \to 0} \frac{- 4 h f^{'} (a - 2 h^{2}) - 3 h^{2} f^{'} (a + h^{3})}{2 h}

= \lim_{h \to 0} \frac{- 4 f^{'} (a - 2 h^{2}) - 3 h f^{'} (a + h^{3})}{2}

= - 2 f^{'} (a)

Commented by naka3546 last updated on 19/Dec/21

H o w t o g e t t h e r e s u l t w i t h o u t L^{'} H o s p i t a l, s i r ?

T h a n k y o u .