To find Σ(x - 1), first calculate (x - 1) for each value:
(3 - 1) + (1 - 1) + (7 - 1) + (4 - 1)
= 2 + 0 + 6 + 3
= 11
A bimodal distribution has two modes, meaning two values occur with the highest and equal frequency.
It indicates the presence of two peaks in the data set.
A parabola is defined as the set of points equidistant from a fixed point (focus) and a fixed line (directrix).
Its eccentricity (e) = 1, which distinguishes it from ellipses (e < 1) and hyperbolas (e > 1).
Given ∫12x⁻⁵ √(-3x⁻⁴ + 1) dx
Let u = -3x⁻⁴ + 1
du/dx = 12x⁻⁵
du = 12x⁻⁵ dx
∫√u du = ∫u^(1/2) du
= (2/3)u^(3/2) + C
Substituting back u = -3x⁻⁴ + 1:
= (2/3)(-3x⁻⁴ + 1)^(3/2) + C
A binomial expression contains exactly two terms, and x² + y² fits that definition.
x²y² is a monomial (single term).
x + y + 1 is a trinomial (three terms).
Mode is the value that occurs most frequently in a dataset.
It represents the most common or popular item in the data.
Commutative property means the order doesn’t matter: 𝐴 ∗ 𝐵 = 𝐵 ∗ 𝐴.
Union ∪ is commutative, so 𝐴 ∪ 𝐵 = 𝐵 ∪ 𝐴.
- f tan xdx = ln[cos x] + C.
This is a standard result from integral calculus involving trigonometric functions.
A small standard deviation means the data is tightly clustered around the mean.
This results in a less spread out (narrower) normal distribution curve.
A critical point occurs where the derivative of a function is zero or does not exist.
These points are important for finding local maxima, minima, or points of inflection.