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:
36 %
Step-by-step explanation:
x% = x/100
27/75 = x/100
100 · 27/75 = 100 · x/100
2700/75 = x
36 = x
36%
Answer:
Step-by-step explanation:
Noah's running speed = 6 mph.
Use formula 
where
D is the distance,
v is the speed,
t is the time.
If 
hour, then 
miles.
If 
hour, then 
miles.
If 
hours, then 
miles.
If 
hours, then 
miles.
If 
hours, then 
miles.
If 
hours, then 
miles.
So, the table is
Answer:
8.94
Step-by-step explanation:
Answer:
12.6 miles I think. I would wait for another answer to be possitive.
