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In this blog we share informations, materials and sample problems regarding competitive examinations on Mathematics.
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# Uniform Continuity of Functions Uniform continuity is a stronger form of continuity that applies uniformly over the entire domain of a function. ## Definition A function $f: A \to \mathbb{R}$ is **uniformly continuous** on $A$ if for every $\varepsilon > 0$, there exists a $\delta > 0$ such that for all $x, y \in A$, $$|x - y| 0$, choose $\delta = \frac{\varepsilon}{2}$. Then for any $x,y$, $$|x-y|
Here we list some of the descriptive type questions asked in various competitive examinations on higher mathematics. We hope these questions will be helpful for the aspirants preparing for upcoming TN Arts and Science college recruitment exam. (The list given is not a final one. Visit the page frequently, as the questions will be updated often.) You can type more questions(missed here) in comment box. They also will be updated. (Updated on 07 June 2024) Algebra: 1. Prove that every group of order $p^2$ is abelian, where $p$ is a prime number. 2. P. T. any group of order 65 must be cyclic. 3. S. T. group of order 30 has a subgroup of order 15. Is it necessarily normal? ******************** Linear Algebra: 1. If T is an nxn matrix that commutes with all nxn matrices, then prove that T is a scalar matrix. 2. Obtain the characteristic polynomial and minimal polynomial for a given matrix. 3. Let A and B be two 3 × 3 complex matrices. Show that A and B ...
