Answer:
∫ₑ°° 1 / (x (ln x)¹⁰) dx
∫₁°° x⁻³ dx
Step-by-step explanation:
A p-series 1 / xᵖ converges if p > 1.
∫ₑ°° 1 / (x (ln x)¹⁰) dx
If u = ln x, then du = 1/x dx.
When x = e, u = 1. When x = ∞, u = ∞.
= ∫₁°° 1 / (u¹⁰) du
p = 10, converges
∫₁₀°° x^(-⅔) dx
= ∫₁₀°° 1 / (x^⅔) dx
p = ⅔, diverges
∫₁°° 2 / x^0.5 dx
= 2 ∫₁°° 1 / x^0.5 dx
p = 0.5, diverges
∫₁°° x⁻³ dx
= ∫₁°° 1 / x³ dx
p = 3, converges
∫₂°° 1/(3x) dx
= ⅓ ∫₂°° 1/x dx
p = 1, diverges
Answer:
2.625
Step-by-step explanation:
2 + 5/8
2 + .625 = 2.625
5/8 = .625
Answer:
6
Step-by-step explanation:
Since we know the side length of the square (6), we can calculate its diagonal using pythagoras.
diag d = √(6²+6²) = 6√2 in
The diagonal is also the diameter of the circle! So the radius of the circle is half of that:
radius r = d/2 = 3√2 in
The area of the circle is πr² = π(3√2)² = 18π in²
4200 * 1.06 = 4452.
4452 * 1.06 = 4719.12.
4719.12 * 1.06 = 5002.27
It would only take 3 years to reach $5000.
