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

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

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Evaluate the Limit ( limit as h approaches 0 of f(x+h)-fx)/h

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

\frac{f ( x , 0 ) ( x + 0 ) - f ( x , 0 ) x}{0}

Solution steps

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

Plug in the value

h = 0

, assuming the function is continuous at this point

= \frac{f ( x , 0 ) ( x + 0 ) - f ( x , 0 ) x}{0}

e^{x}

x^{2}

sin (2 x)

tan (x)

cos (x)

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