Answer:
7
Step-by-step explanation:
13 - [(3² x 4) - 30]
13 - [(9 x 4) - 30]
13 - (36 - 30)
13-6
7
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Example: Suppose you have a rectangle of length 8 and width 6. This figure is also a parallelogram. There are two sides that are of length 6; these are the "opposite sides" of the parallelogram. There are two sides that are of length 8; these are also "opposite sides" of the parallelogram.
3 to the power of 5 to the power of 2-3 to the power of 0 is 9 because 3 to the power of 0 is one and 2 minus one is one and 2 to the power of one is two and 3 to the power of 2 is 9
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
