Let f(x)=8/x.
Then the expression f(x+h)−f(x)/h can be written in the form
A/(x+h),
where A is a constant and A=
Using your answer from above we have:
limh→0f(x+h)−f(x)/h=

Question

Let f(x)=8/x. 
Then the expression f(x+h)−f(x)/h can be written in the form
A/(x+h),
where A is a constant and A=  
Using your answer from above we have: 
limh→0f(x+h)−f(x)/h=

anonymous · Answer

A=????

hero · Answer

$$f(x) = \frac{8}{x}$$$$f(x+h) = \frac{8}{x + h}$$
$f(x+h) - f(x) = \dfrac{8}{x + h} - \dfrac{8}{x}$ 
                        
                         $ = \dfrac{8x}{x(x + h)} - \dfrac{8(x+h)}{x(x+h)}$
                         
                         $=\dfrac{8x - 8(x+h)}{x(x+h)}$
                         
                          $=\dfrac{8x - 8x -8h}{x(x + h)}$

                          $=\dfrac{-8h}{x(x+h)}$

$\dfrac{f(x+h) - f(x)}{h} = \dfrac{\frac{-8h}{x(x+h)}}{h}$
                          
                          $=\dfrac{-8h}{x(x+h)} \div h$
             
                          $=\dfrac{-8h}{x(x+h)} \times \dfrac{1}{h}$

                          $=\dfrac{-8}{x+h}$

Thus $A = -8$

And 
$\lim_{h \to 0} \dfrac{f(x+h) - f(x)}{h} = \dfrac{-8}{x + 0} = -\dfrac{8}{x}$