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.

answer: y = 3/2 x - 3

y = 1/8 x - 3/4 that would be your correct option

step-by-step explanation: w