Question

given the lim as x goes to a of (mx+b) then find the corresponding delta>0 for all epsilon>0

Answer 1

\[\lim_{x \rightarrow a} (mx+b) \]

Answer 2

\[0<|x-a|<\delta\]

want \[|mx+b-ma-b|<\epsilon\]



\[|mx+b-ma-b|=|m(x-a)|=|m||x-a|<\epsilon\]


\[|x-a|<\frac{\epsilon}{|m|}\]

so pick \[\delta=\frac{\epsilon}{|m|}\]

Answer 3

Great praise Master Zarkon *Bows in respect*