The discussion centers on justifying the inequality |lim(x-->0)(f(x))|≤lim(x-->0)|f(x)| for a continuous function f. The participant confirms that the absolute value function, defined as |\ |:\mathbb{R}\rightarrow \mathbb{R}:x\rightarrow |x|, is continuous. They conclude that since the absolute value is continuous, it follows that |lim(x-->0)(f(x))| equals lim(x-->0)|f(x)|, which is supported by established theorems in calculus.
PREREQUISITESStudents of calculus, mathematics educators, and anyone seeking to deepen their understanding of limits and continuity in mathematical analysis.
mike1988 said:I am trying to solve a question and I need to justify a line in which |lim(x-->0)(f(x))|≤lim(x-->0)|f(x)| where f is a continuous function.
Any help?
Ray Vickson said:Show your work. Where are you stuck?
RGV