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Hi is the answer so this makes it okay to do thing when you have it
In this question (brainly.com/question/12792658) I derived the Taylor series for
about
:

Then the Taylor series for

is obtained by integrating the series above:

We have
, so
and so

which converges by the ratio test if the following limit is less than 1:

Like in the linked problem, the limit is 0 so the series for
converges everywhere.
Answer:

Step-by-step explanation:
step 1
Find the volume of the cylinder
The volume of the cylinder is equal to

we have
---> the radius is half the diameter

substitute

step 2
Find the volume of the cone
The volume of the cone is equal to

we have
we have
---> the radius is the same that the radius of the cylinder

substitute

step 3
Find the volume of the plastic object
we know that
The volume of the plastic object is equal to the volume of the cylinder minus the volume of the cone
so

assume


The equation to show the depreciation at the end of x years is

Data;
- cost of machine = 1500
- annual depreciation value = x
<h3>Linear Equation</h3>
This is an equation written to represent a word problem into mathematical statement and this is easier to solve.
To write a linear depreciation model for this machine would be
For number of years, the cost of the machine would become

This is properly written as

where x represents the number of years.
For example, after 5 years, the value of the machine would become

The value of the machine would be $500 at the end of the fifth year.
From the above, the equation to show the depreciation at the end of x years is f(x) = 1500 - 200x
Learn more on linear equations here;
brainly.com/question/4074386