<P> Formal definitions , first devised in the early 19th century , are given below . Informally , a function f assigns an output f ( x ) to every input x . We say the function has a limit L at an input p : this means f ( x ) gets closer and closer to L as x moves closer and closer to p . More specifically , when f is applied to any input sufficiently close to p , the output value is forced arbitrarily close to L. On the other hand , if some inputs very close to p are taken to outputs that stay a fixed distance apart , we say the limit does not exist . </P>
when does a limit of a function not exist
if some inputs very close to p are taken to outputs that stay a fixed distance apart