Use a Maclaurin series to obtain the Maclaurin series for the given function. f(x)= 14x cos(1/15x^2)

Step-by-step explanation:

In order to find this Maclaurin series, we can start by using a known Maclaurin series and modify it according to our function. A pretty regular Maclaurin series is the cos series, where:

So all we need to do is include the additional modifications to the series, for example, the angle of our current function is: so for

the modified series will look like this:

So we can use some algebra to simplify the series:

which can be rewritten like this:

So finally, we can multiply a 14x to the series so we get:

We can input the x into the series by using power rules so we get:

And that will be our answer.

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.