Continuity

Practice Questions – Continuity (Exam-Focused) Question 1. If [f(x)=\dfrac{|x-2|}{x-2},; x\neq 2,][\quad] [\text{and}\quad f(2)=0,] show that (f(x)) is continuous everywhere except…

Concept Overview A function is defined on an interval. If the function has endpoints (like ([a, b])), we cannot check

Practice Questions — Continuity at a Point Question 1. Check the continuity of $ \displaystyle f(x)=\left\{ {\begin{array}{*{20}{c}} {2x+3,} & {x<0}

Question 1 Discuss continuity of $ \displaystyle f(x)=\left\{ \begin{array}{l}x+1,\text{ }x<1\\2,\text{ }\text{ }x<1\\{{x}^{2}},\text{ }x\ge 1\end{array} \right.$ at [x = 1]. Solution

1. Statement of the Concept — What is Continuity of a Function? A function [f(x)] is continuous on an interval

1. Concept Overview: What is Continuity? A function is said to be continuous at a point if its graph has