Final answer:
The largest interval i is the domain where the solution is valid. For a summation changing to an integral, the limit may be all real numbers. In contrast, in quantum mechanics, the domain can be discrete depending on quantization.
Step-by-step explanation:
The largest interval i over which the solution is defined refers to the domain in which the function or solution is valid, continuous, and unambiguous. This interval can vary depending on the specific function or differential equation in question.
For instance, when a limit is taken as a variable approaches zero and the number of steps approaches infinity, transitioning from a summation to an integral, the domain or interval may involve all real numbers or maybe restricted based on the integrand's properties.
In finding the location f₁ of the first focus F₁, by setting dᵢ = ∞, one must use the related lens-maker's equation which often has limitations based on the physical constraints of the lens, such as the refractive indices and the radius of curvature R.
For the provided solution involving quantum numbers and Angular momentum L, the interval i is contingent upon the possible values of m₁, which is given by m₁ = +1, 0, or -1. Here, the context settles L's value using the formula L = √√ℓ(1 + 1) h, and the domain is defined by the discrete, quantized nature of Angular momentum in quantum mechanics.