Question

Can you help me please I just paid 100 dollar for the tutor version and I can’t find one tutor

Answer 1

The Solution.

Given the function below:

`f(x)=(1)/(x+9)\text{ and the interval \lbrack{}10,10+h\rbrack}`

The average rate of change in the given interval is

`\text{Average rate of change}=(f(b)-f(a))/(b-a)`

In this case,

`a=10,b=10+h`

So,

`f(a)=f(10)=(1)/(10+9)=(1)/(19)`
`f(b)=f(10+h)=(1)/(10+h+9)=(1)/(19+h)`

Substituting in the formula, we have

`\text{Average rate of change =}((1)/(19+h)-(1)/(19))/(10+h-10)`
`\begin{gathered} \text{Average rate of change =}((19-(19+h))/(19(19+h)))/(h)=(-h)/(19h(19+h))=(-1)/(19(19+h)) \\ \end{gathered}`

So, the correct answer is

`(-1)/(19(19+h))`