Answer:
The estimate of In(1.4) is the first five non-zero terms.
Step-by-step explanation:
From the given information:
We are to find the estimate of In(1 . 4) within 0.001 by applying the function of the Maclaurin series for f(x) = In (1 + x)
So, by the application of Maclurin Series which can be expressed as:
Let examine f(x) = In(1+x), then find its derivatives;
f(x) = In(1+x)
f'(0)
f ' ' (x)
f ' ' (x)
f ' ' '(x)
f ' ' '(x)
f ' ' ' '(x)
f ' ' ' '(x)
f ' ' ' ' ' (x)
f ' ' ' ' ' (x)
Now, the next process is to substitute the above values back into equation (1)
To estimate the value of In(1.4), let's replace x with 0.4
Therefore, from the above calculations, we will realize that the value of as well as
which are less than 0.001
Hence, the estimate of In(1.4) to the term is is said to be enough to justify our claim.
∴
The estimate of In(1.4) is the first five non-zero terms.