Harmonic functions, defined as twice continuously differentiable functions satisfying Laplace’s equation, have long been a subject of intense study in both pure and applied mathematics. Their ...

This article studies an asymptotic framework for conducting inference on parameters of the form ϕ(θ₀), where ϕ is a known directionally differentiable function and θ₀ is estimated by θ̂n. In these ...

Let X be a normed linear space, Un an n-dimensional Chebyshev subspace of X. For f ∈ X denote by p(f) ∈ Un its best approximation in Un. The problem of strong unicity consists in estimating how fast ...

If \(f\) is differentiable on \([-1,1]\) then \(f\) is continuous at \(x=0\text{.}\) If \(f'(x)\lt 0\) and \(f"(x)>0\) for all \(x\) then \(f\) is concave down ...

Maths Continuity and Differentiability Formulas: Calculus comprises nearly half of the curriculum of the CBSE class 12 mathematics syllabus. Chapter 5 Continuity and Differentiability is one of the ...

Provides a rigorous treatment of topics covered in Calculus 1 and 2. Topics include convergent sequences; continuous functions; differentiable functions; Darboux sums, Riemann sums, and integration; ...

CBSE 2025 Competency-Based Questions: The Central Board of Secondary Education (CBSE) has officially released the practice question paper for the academic year 2024-25, for the class 12th on its ...