Answer:
The value of n for (a) n=425. (b) n=0.
Step-by-step explanation:
Given integration is,
(a) For Trapezoidal Rule : Composite error is,
Where, f''(x_m)=greatest value of |f''(x)|= |4|=4, a=-3, b=3. Therefore to find the minimum number of subinterval,
|
According to the question, we must choose n such that,
So we can take n=425.
(b) For Simpson 1/3 rule : Composite error is,
where,
In this problem , so that,
that is there exist no error. So n=0.
Answer:
The barrel now is more than 1/4 full
Step-by-step explanation:
* A large barrel of oil is 1/4 full.
* Then for 7 1/2 minutes, oil is added to the barrel at a rate of
4.5 gallons per minute.
* Then for 6 1/2 minutes, some of the oil is removed at a rate of
-3 1/2 gallons per minute.
* We need to know The oil in the barrel now is more or less than
1/4 full
* To know that calculate the quantity of oil added in the barrel and the
quantity of oil removed from the barrel.
* <em>If the quantity of oil add is greater than the quantity of oil removed </em>
<em> then, the barrel is more than 1/4 full</em>
* <em>If the quantity of oil removed is greater than the quantity of oil </em>
<em> added then, the barrel is less than 1/4 full</em>
∵ The oil is added to the barrel at a rate of 4.5 gallons per minute
for minutes
∴ The quantity of oil add = 4.5 × 7.5 = 33.75 gallons
∵ The oil is removed from the barrel at a rate of -3.5 gallons per minute
for minutes
∴ The quantity of oil removed = -3.5 × 6.5 = -22.75 gallons
The negative sign to know that this quantity is removed
∵ The quantity of oil add is greater than the quantity of oil removed
∴ The barrel now is more than 1/4 full
