Final answer:
The limit of the function as x approaches zero is undefined.
Step-by-step explanation:
The limit of a function as x approaches zero of x + c/(1-e^x) can be found by substituting zero into the function. This gives us 0 + c/(1-e^0). Since e^0 is equal to 1, the limit becomes c/(1-1). Since any number divided by zero is undefined, the limit of the function as x approaches zero is undefined.