a function with a limit that as x goes to 0 the function equals 1 but f(0) is not 0. please! any function +why

Question

sorry thats wrong the end should be f(0) is nt equal to 1. ie if you fill 0 into the equation the answer cant be 1

Answer 1

one such function is (sinx)/x
limit of the function as x approaches 0 is 1,this can be proved, refer any book on calculus for the proof.
but at x=0 function is not defined.

Answer 2

Let f(x)=x+1 for x not equal to 0 and set f(0)=0.

Answer 3

Think of a function with a jump discontinuity at 0.

Answer 4

needless to say, any a no longer equivalent to 0 will paintings. If we'd go with to circumvent the three factors, any b no longer equivalent to 0 will paintings too. all of us understand this simply by fact for the functionality to bypass by way of those 3 factors might might desire to have a a million/2-era or finished era equivalent to 3. If it does, it won't bypass by way of (0,0) which it would desire to do for x = 0.