Teaching AWES Army Public School TGT Mock Test 2024 Mathematics Limit and Continuity Continuity of a function
Consider the following in respect of the function \({\rm{f}}\left( {\rm{x}} \right) = {\rm{\;}}\left\{ {\begin{array}{*{20}{c}} {2 + {\rm{x}},{\rm{\;\;x}} \ge 0}\\ {2 - {\rm{x}},{\rm{\;\;x}} < 0} \end{array}} \right.\)
1. \(\mathop {\lim }\limits_{{\rm{x}} \to 1} {\rm{f}}\left( {\rm{x}} \right)\) does not exist.
2. f(x) is differentiable at x = 0
3. f(x) is continuous at x = 0
Which of the above statement is/are correct?1
1 only
2
3 only
3
2 and 3 only
4
1 and 3 only