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
Sum means add
difference means subttract
x+y=1
x-y=11
add the 2 equations together
2x+0y=12
divide 2
x=6
subitute
6+y=1
subtract 6
y=-5
x=6
y=-5
A₁ = 3
a₂ = 4.2
d = a₂ - a₁
= 4.2 - 3
= 1.2
a₉₈ = a₁ + d(n-1)
= 3 + 1.2(98-1)
= 3 + 1.2×97
= 3 + 116.4
= 119.4
Answer:
And we can find this probability using the normal standard table with this difference:
Step-by-step explanation:
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
Where 
and 
We are interested on this probability
And we can solve the problem using the z score formula given by:
Using this formula we got:
And we can find this probability using the normal standard table with this difference:
(10-7)=3
(8-4)=4
3*4=12
I hope this helps :)
