What is the limit as h approaches 0 of ((f(h)(0+h)-f(0)))/h ?

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

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

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

Undefined

Solution steps

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}

Simplify

\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)

With the exception of indeterminate form

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

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

Undefined

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

= - Undefined + f \cdot 0

= Undefined

\int x f (x) d x

f (x) = 17 e^{x}

f (x) = - x^{2} + 4 x, at x = 1

\frac{x d y}{d x} + 5 y = x^{3} - x

\int_{0}^{1} \frac{e ^{x} + 1}{e ^{x} + x} d x

What is the limit as h approaches 0 of ((f(h)(0+h)-f(0)))/h ?
The limit as h approaches 0 of ((f(h)(0+h)-f(0)))/h is Undefined