Teaching HTET PGT Level 3 - 2024 Mock Test Mathematics Limit and Continuity Continuity of a function
A function is defined as follows:
\({\rm{f}}\left( {\rm{x}} \right):\left\{ {\begin{array}{*{20}{c}} { - \frac{{\rm{x}}}{{\sqrt {{{\rm{x}}^2}} }},{\rm{\;x}} \ne 0}\\ {0.{\rm{\;x}} = 0} \end{array}} \right.\)
Which one of the following is correct in respect of the above function?
1
f(x) is continuous at x = 0 but not differentiable at x = 0
2
f(x) is continuous as well as differentiable at x = 0
3
f(x) is discontinuous at x = 0
4
None of the above