lim as x goes to 1 (x^(2)-2x+4)=3
Using what "basis"? If you know about "continuous functions" and in particular that all polynomials are continous for all values of x then it is sufficient to say, as emakarov does, that the limit is .
If, on the other hand, you have only the definition of limit to work with, you need to look at , then what can you say if you choose so that becomes ?