The integral of 1/x is ln|x| + C.

The integral of 3x^2 is (3/3)x^3 + C = x^3 + C.

The integral of x^n dx is (x^(n+1))/(n+1) + C.

The integrating factor is e^(∫3dx) = e^(3x).

The IUPAC name for CH3-CH2-COOH is propanoic acid, as it has three carbon atoms in the longest chain.

The IUPAC name for CH3COOH is acetic acid.

Latent heat of fusion (L) = Q / m = 334,000 J / 500 g = 668 J/g.

Latent heat of fusion (L) = Q/m = 2400 J / 80 g = 30 J/g.

The North Pole is located at 90°N latitude.

The latus rectum of a parabola y^2 = 4px is given by 4p. Here, 4p = 12, so p = 3, and the latus rectum is 4p = 12.

LCM of 4 and 6 is 12.

Arc length = (θ/360) × 2πr = (60/360) × 2π(7) = (1/6) × 14π = 7π/3 cm.

Arc length = (θ/360) × 2πr = (60/360) × 2π(5) = (1/6) × 10π = 5π/6 cm.

In a right triangle, the altitude from the right angle to the hypotenuse is equal to the length of the other side. Thus, the altitude is 6 cm.

Using Heron's formula, the area is 30 cm². The altitude = (2 * Area) / base = (2 * 30) / 13 = 6 cm.

The length of the diagonal d of a rectangle can be found using the Pythagorean theorem: d = √(length² + width²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

Diagonal = √(length² + width²) = √(3² + 4²) = √(9 + 16) = √25 = 5 cm

Diagonal = √(length² + width²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm

Area = πr². Given area = 50π, r² = 50, r = √50 = 5√2. Diameter = 2r = 10√2 units.

Using the distance formula, length = sqrt((7-3)^2 + (1-4)^2) = sqrt(16 + 9) = 5.

In an equilateral triangle, the median is equal to the side length, so it is 10 cm.

Using the median formula: m_a = 1/2 * sqrt(2b^2 + 2c^2 - a^2), where a = BC, b = AC, c = AB. m_a = 1/2 * sqrt(2*6^2 + 2*10^2 - 8^2) = 7 cm.

Using the identity 1 - cos(x) = 2sin^2(x/2), we have lim (x -> 0) (1 - cos(x))/(x^2) = lim (x -> 0) (2sin^2(x/2))/(x^2) = 1/2.

Using the Taylor series expansion for cos(x), we find that lim (x -> 0) (cos(x) - 1)/x^2 = -1/2.

Using the derivative of e^x at x = 0, we find that lim (x -> 0) (e^x - 1)/x = 1.

Using L'Hôpital's Rule, we differentiate the numerator and denominator to find lim (x -> 0) (1/(1 + x)) = 1.

Using the limit lim (x -> 0) (tan(x)/x) = 1, we have lim (x -> 0) (tan(3x)/x) = 3 * lim (x -> 0) (tan(3x)/(3x)) = 3.

Factoring gives (x - 1)(x + 1)/(x - 1), which simplifies to x + 1. Thus, lim (x -> 1) (x + 1) = 2.

The total difference is 60° + 120° = 180°. This is 12 hours difference. Therefore, 6:00 AM + 12 hours = 6:00 PM.

120°E is 120/15 = 8 hours ahead. Therefore, 3:00 PM + 8 hours = 11:00 PM.