C and D is true and others are false
1. C = 10π; A = 25π
2. 254.34
3. 12
4. without a picture it is just a shot 390 mm3
5. 12
Step-by-step explanation:
(a) ∫₋ₒₒ°° f(x) dx
We can split this into three integrals:
= ∫₋ₒₒ⁻¹ f(x) dx + ∫₋₁¹ f(x) dx + ∫₁°° f(x) dx
Since the function is even (symmetrical about the y-axis), we can further simplify this as:
= ∫₋₁¹ f(x) dx + 2 ∫₁°° f(x) dx
The first integral is finite, so it converges.
For the second integral, we can use comparison test.
g(x) = e^(-½ x) is greater than f(x) = e^(-½ x²) for all x greater than 1.
We can show that g(x) converges:
∫₁°° e^(-½ x) dx = -2 e^(-½ x) |₁°° = -2 e^(-∞) − -2 e^(-½) = 0 + 2e^(-½).
Therefore, the smaller function f(x) also converges.
(b) The width of the intervals is:
Δx = (3 − -3) / 6 = 1
Evaluating the function at the beginning and end of each interval:
f(-3) = e^(-9/2)
f(-2) = e^(-2)
f(-1) = e^(-1/2)
f(0) = 1
f(1) = e^(-1/2)
f(2) = e^(-2)
f(3) = e^(-9/2)
Apply Simpson's rule:
S = Δx/3 [f(-3) + 4f(-2) + 2f(-1) + 4f(0) + 2f(1) + 4f(2) + f(3)]
S ≈ 2.5103
Answer:
3/4 becaus ecant simplify it more
Step-by-step explanation:
<span>Let x = first number
Let y = second number
x + y = 4
x * y = (-12)
Solve the first equation for x.
x = 4 - y
Now substitute this value of x into the second equation.
(4 - y) * y = (-12)
4y - y² = (-12)
y² - 4y - 12 = 0
(y + 2) * (y - 6) = 0
Now set both polynomials equal to zero
y + 2 = 0
y = -2
y - 6 = 0
y = 6
If you substituted these two values for y into either equation and solve for x, you would get the combination of 6 and -2
Hope I was able to help you! :)
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