limit as h approaches 0 of ((f(h)(0+h)-f(0)))/h

解

h \to 0 lim (\frac{( f ( h ) ( 0 + h ) - f ( 0 ) )}{h})

未定義

解答ステップ

h \to 0 lim (\frac{f ( h ) ( 0 + h ) - f ( 0 )}{h})

f (h) (0 + h) - f (0) = f (h) (0 + h) (1 - \frac{f ( 0 )}{f ( h ) ( 0 + h )})

= h \to 0 lim \frac{f ( h ) ( 0 + h ) ( 1 - \frac{f ( 0 )}{f ( h ) ( 0 + h )} )}{h}

簡素化

\frac{f ( h ) ( 0 + h ) ( 1 - \frac{f ( 0 )}{f ( h ) ( 0 + h )} )}{h} : - \frac{f ( 0 )}{h} + f (h)

= h \to 0 lim (- \frac{f ( 0 )}{h} + f (h))

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

不定形式の場合を除く

= - h \to 0 lim (\frac{f ( 0 )}{h}) + h \to 0 lim (f (h))

h \to 0 lim (\frac{f ( 0 )}{h}) =

未定義

h \to 0 lim (f (h)) = f (0)

= - 未定義 + f \cdot 0

= 未定義