Question

Show that limf(x) x--->c = L

if and only if limf(h+c) h--->0 =L

Answer 1

can you use equation to write the problem please

Answer 2

\[\lim_{x \rightarrow c}f(x)=L \rightarrow \lim_{h \rightarrow 0}f(h+c)=L\]

Answer 3

well if
\[\lim_{x \rightarrow c}f(x) =L \Leftrightarrow \lim_{x \rightarrow c^{+}}f(x) =L \text{ and } \lim_{x \rightarrow c^{-}}f(x) =L\]
let x = c+h so that x-c = h. then as x->c, h->0
and then rewrite