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.
First we need to find f(2) and f(5), which are 5 and 11 respectively; all you have to do is plug in 2 and 5.
Then, we use the following formula:
(f(b)-f(a))/(b-a),
where b and a are the largest and smallest x values respectively.
Finally, we plug our values in:
(11-5)/(5-2)=6/3=2
In fact, the average rate of change of any linear function is just the coefficient of the x term. Hope this helped!
F, D, C
F: 5 x 3 = 15
D: 7 x 3= 21 - 2 = 19
C: 5 x 3 = 15 + 6 = 21
Price of DVD player ≥ $150
Saved = $80
Amount needed = $150 - $80 = $70
Saving per week = $10
Let x be the number of weeks needed:
80 + 10x ≥ 150
10x ≥ 150 - 80
10x ≥ 70
x ≥ 70 ÷ 10
x ≥ 7
Answer: She needs to save for for at least 7 weeks.