Answer to Question #195743 in Real Analysis for Dharaba Parmar

Question

Give an example of a function in L₃[1 2] that is not in C [1 2]

Answer 1

$f(x)=\frac{1}{x-1.5}$

$(f(x))^3$ is integrable on $[1,2]$ , so $f(x)\isin L_3[1,2]$

$f(x)$ is not continious on $[1,2]$ , so $f(x)\notin C[1,2]$