Could someone please check my work

let f:0 - R and let c be on accumulation point of D. Suppose That f has a limit at C. Prove That f is bounded on a neighborhood of c. That is prove That There exists a neighborhood U of c and a real number M such That DAUO If(x)/sm for all XEUND. Suppose fid - 1R and c is an accumulation point of is and f has a limit at c. Let XEUND. Then by The definition of intersection, XEU of c and XED. Since XEU of C, Then by The definition of deleted neighborhood of x, 06/ x-c/28 . Since XED and OL/x-c/o There exists a 820 Such That / f ( x)- L/