Nov 12, 2012 Thread starter #1 D dwsmith Well-known member Feb 1, 2012 1,673 $f(x) = \frac{\sin x}{x}$ if $x\neq 0$, $f(0) = 0$. We know that the $\lim\limits_{n\to 0}f(x) = 1$. Since $f(0) = 0$, we will have a jump discontinuity. Is this correct reasoning?
$f(x) = \frac{\sin x}{x}$ if $x\neq 0$, $f(0) = 0$. We know that the $\lim\limits_{n\to 0}f(x) = 1$. Since $f(0) = 0$, we will have a jump discontinuity. Is this correct reasoning?
Nov 12, 2012 #2 Sudharaka Well-known member MHB Math Helper Feb 5, 2012 1,621 dwsmith said: $f(x) = \frac{\sin x}{x}$ if $x\neq 0$, $f(0) = 0$. We know that the $\lim\limits_{n\to 0}f(x) = 1$. Since $f(0) = 0$, we will have a jump discontinuity. Is this correct reasoning? Click to expand... No this is a removable discontinuity.
dwsmith said: $f(x) = \frac{\sin x}{x}$ if $x\neq 0$, $f(0) = 0$. We know that the $\lim\limits_{n\to 0}f(x) = 1$. Since $f(0) = 0$, we will have a jump discontinuity. Is this correct reasoning? Click to expand... No this is a removable discontinuity.
