Sentence examples for instantaneous rate of change from inspiring English sources

Newton referred to a varying (flowing) quantity as a fluent and to its instantaneous rate of change as a fluxion.

With the technical preliminaries out of the way, the two fundamental aspects of calculus may be examined: a. Finding the instantaneous rate of change of a variable quantity.

We just found, in differential calculus terms, the derivative function df(x)/dx, or instantaneous rate of change, at any point x, of the function f(x)=x3, which is 3x2.

If, as h becomes smaller and smaller, this slope tends to a limiting value, then the direction of the chord stabilizes and the chord approximates more and more closely the tangent to the graph at t. Thus, the numerical notion of instantaneous rate of change of f(t) with respect to t corresponds to the geometric notion of the slope of the tangent to the graph.

How do you find instantaneous rate of change?

The instantaneous rate of change of state probabilities can be derived as, d d t P j ( t ) = ∑ i = 1 S P i ( t ) λ i j (7).

Calculus, branch of mathematics concerned with the calculation of instantaneous rates of change (differential calculus) and the summation of infinitely many small factors to determine some whole (integral calculus).

Instantaneous acceleration (at a precise moment and location) is given by the limit of the ratio of the change in velocity during a given time interval to the time interval as the time interval goes to zero (see analysis: Instantaneous rates of change).

Less directly, it is related to the extremely important question of the calculation of instantaneous velocity or other instantaneous rates of change, such as the cooling of a warm object in a cold room or the propagation of a disease organism through a human population.

Three additional considerations are required to successfully control crystallization process local conditions rather than bulk, instantaneous rates of change rather than mean values that control the relative rates of nucleation, and crystal growth.

The non-diagonal elements q ij are the instantaneous rates of change from amino acid i to amino acid j and diagonal elements q ii are such that each matrix row sums up to 0. Q can be calculated by: Q = S* diag     (3) S is the matrix of amino acid exchangeability parameters [ 39]. π i is the equilibrium frequency for amino acid i.