#[Let][Sea]# $f(x) = %0$. #[We are going to compute the average rates of change of $f$ over the following smaller and smaller intervals $[%1,%1+h]$, where $h = 1,\ 0.1,\ 0.01,\ 0.001, 0.0001$. This means that we are going to compute the rate of change of $f$ over each of the following smaller and smaller intervals:][Vamos a calcular las razones de cambio promedio de $f$ en los siguientes intervalos cada vez más pequeños $[%1,%1+h]$, donde $h = 1,\ 0.1,\ 0.01,\ 0.001, 0.0001$. Esto significa que vamos a calcular la tasa de cambio de $f$ en cada uno de los siguientes intervalos cada vez más pequeños:]#
$[%1,%4[1]]$ \t $h = 1$, #[so][por lo que]# $[%1,%1+h] = [%1,%4[1]]$ \\ $[%1,%4[2]]$ \t $h = 0.1$, #[so][por lo que]# $[%1,%1+h] = [%1,%4[2]]$ \\ $[%1,%4[3]]$ \t $h = 0.01$, #[so][por lo que]# $[%1,%1+h] = [%1,%4[3]]$ \\ $[%1,%4[4]]$ \t $h = 0.001$, #[so][por lo que]# $[%1,%1+h] = [%1,%4[4]]$ \\ $[%1,%4[5]]$ \t $h = 0.0001$, #[so][por lo que]# $[%1,%1+h] = [%1,%4[5]]$
Now fill in the missing values below, accurate to four decimal places. (You can use the for this task.)
$\bold{h}$ \t Avg. Rate of Change
over $\bold{[a,a+h]}$ \\ $%2[1]$ \t BOX \\ $%2[2]$ \t BOX \\ $%2[3]$ \t BOX \\ $%2[4]$ \t BOX \\ $%2[5]$ \t BOX \\ $\color{indianred}{0}$ \t #[Not defined][No definida]#
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Do you see a trend? First, we notice an interesting pattern in the decimal places as h gets smaller and smaller. Also, we see that the average rates of change are getting closer and closer to the value BOX
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RANDOMIZE