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## Homework Statement

With reference to this graph:

http://imageshack.us/photo/my-images/41/deletemev.jpg/

Is the value of c that makes lim x->1 [f(x) + c g(x)] exist equal to the same value of c that makes f(x) + c g(x) continuous at x = 1?

## Homework Equations

## The Attempt at a Solution

They're the same, right, because the value of c that makes the lim x->1 of f(x) + cg(x) exist is the same as the value of c that makes f(x) + cg(x) continuous at x=1? Or could I be wrong??