Find the sum: 1/6 + 2/3
2 answers:
You might be interested in
Answer:
a) integral = 24.72
b) |Error| ≤ 0.4267
Step-by-step explanation:
a)
The integral:
can be approximated with the midpoint rule, as follows:
6.7*(0.8 - 0.0) + 8.9*(1.6 - 0.8) + 6.9*(2.4-1.6) + 8.4*(3.2 - 2.4) = 24.72
(that is, all the intervals are 0.8 units length and f(x) is evaluated in the midpoint of the interval)
b)The error bound for the midpoint rule with <em>n</em> points is:
|Error| ≤ K*(b - a)^3/(24*n^2)
where <em>b</em> and are the limits of integration of the integral and K = max |f''(x)|
Given that -5 ≤ f''(x) ≤ 1, then K = 5. Replacing into the equation:
|Error| ≤ 5*(3.2 - 0)^3/(24*4^2) = 0.4267
Solve <span>4x − 3y = 3 and 5x − 4y = 3
Step 1: Solve for x in 4x-3y=3:
4x-3y=3
4x-3y+3y=3+3y [Add 3y to both sides]
4x=3y+3
</span>
[Divide both sides by 4]
x=
Step 2: Substitute
<span> for x in 5x-4y=3
5x-4y=3
5(</span><span>)-4y=3
</span>
[Subtract 
to both sides]
[Divide both sides by 
]
<span>y = 3
Step 3: Substitute 3 for y in x = </span>
x = 3
Step 1: Solve for x in 4x-3y=3:
4x-3y=3
4x-3y+3y=3+3y [Add 3y to both sides]
4x=3y+3
</span>
x=
Step 2: Substitute
5x-4y=3
5(</span>
</span>
<span>y = 3
Step 3: Substitute 3 for y in x = </span>
x = 3